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UBC Theses and Dissertations

Studies of c-type RR Lyrae stars Mendes de Oliveira, Cláudia Lúcia 1988

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S T U D I E S O F C - T Y P E R R L Y R A E S T A R S By C L A U D I A L U C I A M E N D E S D E O L I V E I R A B . S c , Universidade Federal de Minas Gerais, Brasil, 1985 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF S C I E N C E in T H E F A C U L T Y OF G R A D U A T E STUDIES Department of Geophysics and Astronomy We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF BRITISH C O L U M B I A August 1988 ©Claudia Oliveira, 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of ^eQ(?Wy .S\ c _S Oy \4 A^'Vr'DYxo vn.' The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) A B S T R A C T Three studies of c-type R R Lyrae stars in the field of the Galaxy and in the Ursa Minor dwarf spheroidal galaxy have been completed. They include a study of the secular period behaviour of the star R U Psc; a determination of new radial velocities for 28 field c-type R R Lyrae stars; and a study of seven variables in the Ursa Minor dwarf galaxy, five of which are c-type R R Lyrae stars. R U Psc (period P=0^3904) is known for irregular cycle-to-cycle brightness vari-ations and a possible 28 day Blazhko period (Tremko 1964). Using data from the literature, from 1956 to 1984, the long period behaviour of the star was analysed and, in particular, the possibility of R U Psc being a double-mode star was investigated. It is concluded that the peculiarities seen in the photometry of R U Psc are not due to secondary oscillations of the sort seen in R R d stars. Radial velocities for 20 field c-type R R Lyrae stars, whose radial velocities previ-ously were unknown, are presented. The typical uncertainties are ± 15 km/s. Seven variable stars in the Ursa Minor dwarf galaxy have been studied using new photometry from 38 C C D frames. Combining these data with photographic photometry from van Agt (1967, 1968), and new photographic data from Nemec, Wehlau and Mendes de Oliveira, (1988, hereafter NWO) , very accurate periods and colours were derived for these seven variables. With accurate mean colours, the blue and red edges of the instability strip could be set with little uncertainty. A distance modulus of (ra — M) o=19.23 ± 0.27 was derived for Ursa Minor from the mean magnitude of - i i -the c-type R R Lyrae stars. Analysing the new photographic data (NWO), four new anomalous Cepheids were found in Ursa Minor bringing to seven the total number of anomalous Cepheids now known. None of the c-type R R Lyrae stars in Ursa Minor, for which sufficient data are available, was found to be a double-mode R R Lyrae star. - i i i -T A B L E O F C O N T E N T S Abstract i i Table of Contents iv List of Tables vi List of Figures vii Acknowledgements ix Introduction 1 Chapter 1. Period Analysis of the RR Lyrae Star RU Piscium 6 1.1 Introduction 6 1.2 New Period Analysis of R U Psc 7 1.3 Discussion and Summary 15 Chapter 2. Radial Velocities of c-Type RR Lyrae Stars 22 2.1 Introduction 22 2.2 Observations and Reductions 24 2.3 Results and Discussion 32 Chapter 3. CCD Photometric Study of Seven Variable Stars in the Ursa Minor Dwarf Galaxy 51 3.1 Introduction 51 3.2 Observations and Reductions 53 3.3 Analysis of the Combined Photographic and C C D Data 66 3.4 Discussion 89 iv 3.5 Summary Bibliography L I S T O F T A B L E S Chapter 1 Table I. Periods for R U Psc 9 Chapter 2 Table II. Standard stars used for cross-correlation 33 Table III. Radial velocities of c-type R R Lyrae stars 34 Chapter 3 Table IV. C C D frames of the Ursa Minor Dwarf Galaxy 54 Table V . Photometry for the calibration stars 57 Table V I . Photometry for the non-variable stars 63 Table VII . B magnitudes for the variables 67 Table VIII. V magnitudes for the variables 68 Table LX. Photometric properties of the seven variables 69 vi L I S T O F F I G U R E S Chapter 1 1 Theta transform for R U Psc using Dezso's data 11 2 Light curve for R U Psc using Dezso's data 12 3 Light curves using Tremko's data from 1961-1963 14 4 Theta transform for R U Psc using a subset of Tremko's data 16 5 Cycle-to-cycle variations on the light curves of R U Psc 17 6 O - C diagram for R U Psc from 1936 to 1969 19 Chapter 2 7 Sample of typical fiat fields 26 8 Typical residuals from the wavelength calibration 28 9 Spectrum of V895 Aql 30 10 Spectrum of V895 Aql with the continuum subtracted 31 11 Galactic positions of the R R Lyraes observed 38 12 Histogram of the velocities of the RRc's observed 41 13 Spectrum of V508 Cyg 45 14 Radial velocity curve for K N Per 47 Chapter 3 15 Ursa Minor stars measured on the C C D frames 55 vii 16 Weighted least squares fit used for calibration of the instrumental system 59 17 Transformations from instrumental to standard system 60 18 Comparisons with OA study and with the P200 pg and P60 pg data 65 19 Period searches for V58 72 20 Period searches for V55 74 21 Light curves for V55 75 22 Period searches for V57 76 23 Light curves for V57 77 24 Light curves for V58 79 25 Period Searches for V59 80 26 Light curves for V59 81 27 Period searches for V83 82 28 Light curves for V83 83 29 Period searches for V95 85 30 Light curves for V95 86 31 Real time light curve for V95 87 32 Period searches for V97 88 33 Light curves for V97 90 34 Colour-magnitude diagram for Ursa Minor 91 35 Searches for double-mode R R Lyrae stars in Ursa Minor 95 36 Period-luminosity diagram for the variables in Ursa Minor, including also the anomalous Cepheids known in other dwarf spheroidals 99 vii i A C K N O W L E D G E M E N T S I would like to thank all the people who have contributed, in various and important ways, to this thesis. In particular, I wish to thank my supervisor Dr. James Nemec, for his constant enouragement, patience, and understanding over the last two years, as well as for the financial support which made this thesis possible. I would also like to thank the staff of the Dominium Astrophysical Observatory for allowing me telescope time and the use of their computing facilities and also for their willingness to answer questions and to assist with the small problems which can make research difficult. I would especially like to thank D A O staff members Douglas Welch and Mike Bolte for reading over parts of the text of this thesis, and for making many helpful suggestions, and David Westpfahl for his assistance. In addition, I was helped, in no small way, by the people who took the time to check over my English grammar and spelling. Without these people, this thesis would never have been completed. I would especially like to thank Gary Brent, Dr. James Nemec, and Gerry Grieve in this regard. I would also like to thank my parents, Laerte Oliveira and Celia Oliveira, who always encouraged me to do my best, and all my friends for their support. Finally, I wish to thank Bernhard Schwarz, without whom I could have never have made it through to see this finished. - ix -I N T R O D U C T I O N The potential of R R Lyrae stars as standard candles for establishing the galactic and extra galactic distance scale has long been recognized. These stars are intrinsically luminous and, as variable stars with periods of less than a day, they are easily identified to long distances. There are numerous known R R Lyraes in the Galactic field and in globular clusters. They have also been identified in nearby dwarf galaxies and recently in major spiral galaxies in the Local Group. R R Lyraes are usually used as distance indicators assuming that they all have approximately the same absolute magnitude. From statistical parallax, the absolute magnitude of an R R Lyrae star is < Mv > = 0^76 ± 0m.14 (Hawley et al. 1986). But this value derived via other methods such as Baade-Wesselink studies (e.g. Jones et al. 1987) and globular cluster main-sequence fitting (e.g. Sandage 1982) varies over a large range, from 0m.3 to lm.0. Also the dependence of the absolute magnitude of R R Lyraes on metal abundance is a controversial matter for which no definite answer has yet been found (for a review on this subject, see Jones et al. 1987). Because crucial problems like these have not yet been solved, R R Lyraes are still one of the most important and fertile fields of study. A brief review of the properties and types of R R Lyrae stars will be useful at this point. R R Lyraes are A to F stars pulsating in radial modes (Schwarzschild 1941) with typical periods in the range 0<*2 to 0^9, and amplitudes between 0™2 and 2m.0. There are four types of R R Lyraes currently identified: Bailey types a, b, c and d. The - 1 -three first classifications were introduced by Bailey in 1895 to distinguish R R Lyraes according to the shape of their light curves. The d-class designation was introduced recently when the first double-mode R R Lyraes were identified. The ab-types (RRab's) are fundamental mode pulsators and they tend to be the coolest R R Lyraes. The a-types have more asymmetric light curves and larger amplitudes than the b-types. The c-types (RRc's) pulsate in the first overtone mode, they usually have sinusoidal light curves and they are the hottest R R Lyraes. The d-types (RRd's) pulsate in the first overtone and fundamental modes simultaneously, the first overtone pulsation being the dominant mode. They are thought to be switching modes and to have temperatures cooler than the c-types but hotter than the ab-types, if no overlap in T eff is seen between the ab- and c-type R R Lyrae stars. The overlap of temperatures of the hottest ab-type R R Lyrae stars with the coolest c-types is very common in Oosterhoff (1939) Type II 1 globular clusters. The same 1Oosterhoff (1939) subdivided the globular clusters into types I and II according to the mean periods of the ab-type R R Lyrae stars. In Oosterhoff type II (Oo II) clusters the mean periods of the RRab's and RRc's are ~ 0^65 and 0dA0 respectively. In Oosterhoff type I (Oo I) clusters the mean periods of the RRab's and RRc's are ~ 0^55 and 0^35 respectively. It was later found that there is a strong correlation between the Oo types and metal abundance. Oo II clusters have [Fe/H] 2.0 and Oo I clusters have [Fe/H]~-1.0. Metal abundance is now the usual criterion for determining the Oosterhoff classification, which also enables field stars to be classified in a similar manner. - 2 -effect is observed in the Ursa Minor Dwarf Galaxy (see chapter 3) but it is usually not observed in Oosterhoff Type I globular clusters. There is very little information avail-able on the overlap of colours (temperatures) between ab- and c-type field R R Lyrae stars. There are three different populations of field R R Lyrae stars. Two are identified as the Oosterhoff types I and II (Oosterhoff 1939) and the third one is a very metal rich group of R R Lyraes that have no cluster counterparts (even the most metal rich clusters usually generate only a few R R Lyrae stars: 47 Tuc, for example, has only 3, and these are Oo type I). These three different populations have been identified among the ab-type R R Lyrae stars very clearly. The field c-type R R Lyrae stars need more study. The field c-type R R Lyraes have periods that range from 0^25 to 0^40. The longest period c-type R R Lyrae stars are metal poor and represent the Oosterhoff type II group. Most of the short period c-type R R Lyrae stars are very metal rich (see Kemper 1982). The short period RRc's represent an interesting field of study by themselves, because of the similarity of the light curves and range in periods of these stars with the ones of dwarf Cepheids and second-mode pulsators. According to Paczynski (1965), a peculiarity that would distinguish the RRc's from the dwarf Cepheids and second-overtone pulsators is the presence of a pre-maximum hump on the light curves. The clear separation of these three classes of stars would be of great interest. The motivation for studying c-type R R Lyrae stars was mainly the lack of infor-- 3 -mation on these stars compared with the RRab's. The only large scale study of c-type R R Lyrae stars is the determination of metal abundances for 66 stars done by Kemper (1982). Eleven of these c-type stars are in common with the study of radial-velocity determinations done in chapter 2 of this thesis. The c-type R R Lyrae stars are essential tools in the studies of the helium abundance variations since they define the blue edge of the instability strip. A detailed study of RRc's is also important because it may lead to the identification of new d-type R R Lyrae stars. There is only one R R d known in the field of the Galaxy and only ~ 40 identified in other systems. The double-mode R R Lyrae stars are specially important because information on their masses and relative metal abundances can be obtained from their periods and period ratios (Petersen 1973; Cox et al. 1980). This thesis is divided into three chapters, two of which are about c-type R R Lyrae stars in the field of the Galaxy. The third one is an analysis of seven variable stars in the Ursa Minor Dwarf Galaxy, five of which are c-type R R Lyrae stars. In chapter I, a new period analysis for the c-type R R Lyrae star R U Psc is presented. The causes for the cycle-to-cycle brightness variations seen in the light curve of the star are investigated. It is concluded that the star is not a double-mode star. This study has already been published in the Publications of the Astronomical Society of the Pacific (Mendes de Oliveira and Nemec 1988). In Chapter II radial-velocity determinations are made for 20 c-type R R Lyrae stars brighter than 15™0 with previously unknown radial velocities. In the third chapter a C C D study of seven variables in the Ursa Minor dwarf spheroidal galaxy is presented. This chapter is part of a larger project of studying all the variable - 4 -stars in the Ursa Minor dwarf galaxy (Nemec, Wehlau and Mendes de Oliveira 1988). By combining the C C D photometry with existing photographic data, accurate colours and periods were derived for the seven variables. A discussion of all the variables in the Ursa Minor dwarf galaxy (RR Lyraes, anomalous Cepheids, possible RRd's and possible second-mode pulsators) is presented. - 5 -C H A P T E R 1 P E R I O D A N A L Y S I S OF T H E C - T Y P E R R L Y R A E STAR R U P I S C I U M 1.1. I N T R O D U C T I O N The c-type R R Lyrae star R U Psc (P~0^3918) is known for its irregular cycle-to-cycle brightness variations and its complicated period change behaviour. Cycle-to-cycle brightness variations and periodic changes in the morphology of the light curves of R R Lyrae stars have been observed for many years. These modulations (periods from ~ 10d to 300d) in the amplitudes of the R R Lyrae stars are known as the Blazhko effect (named after Blazhko 1907) and are usually seen in the short period ab-type R R Lyrae stars. Approximately 30% of ab-type R R Lyrae stars are Blazhko variables. Among the c-type R R Lyrae stars, however, the Blazhko effect is a rare phenomenum. According to Szeidl (1975) there are only three RRc's that exhibit such an effect: R U Psc, B V Aqr and T V Boo. A more common effect in c-type R R Lyrae stars is the presence of a simultaneous low-amplitude second mode of oscillation with period such that the ratio of the first overtone to the fundamental period is P\/Po ~ 0.746. The effect on the light curve of these stars is, as in the Blazhko effect, an additional scatter that hides the second oscillation. These are called double-mode R R Lyrae stars (RRd's). Since 1981 over 40 double-mode R R Lyrae stars have been identified. Of these, only one, A Q Leo (Jerzykiewicz and Wenzel 1977; Jerzykiewicz, Schult and Wenzel 1982), is not in a - 6 -distant globular cluster or dwarf galaxy. The rewards of finding other R R d stars in the nearby field of the Galaxy are obvious: (1) because of their brightness, high signal-to-noise ratio (S/N) and high dispersion spectroscopic observations could be made to further study their physical characteristics; (2) since very metal rich R R Lyrae stars are not present in globular clusters, one might be able to extend to higher metal abundances the mass-metal abundance relationship for R R d stars (see Clement et al. 1986) and; (3) they could provide better tools for the investigation of the relationship (if any) between the mechanism that causes the cycle-to-cycle variations seen in Blazhko variables and the mechanism causing the simultaneously excited multiperiodic oscillations of R R d stars. In the present chapter, photometry from the literature is used to study the period behaviour of the low-amplitude (AB= 0m.50) c-type R R Lyrae star R U Psc. The light curves of R U Psc showing a large scatter presented by Dezso (1945) and Tremko (1964) suggested that this star could be a candidate double-mode pulsator and that a search for a secondary oscillation of the sort seen in previously identified RRd's should be made. In § 1.2 the photometry used for the analysis and the period search techniques are described. Section 1.3.1 presents a discussion about Blazhko variations, § 1.3.2 shows an O-C diagram for R U Psc using all the available data and § 1.3.3 summarizes the results and conclusions. 1.2. N E W P E R I O D A N A L Y S I S OF R U P I S C I U M R U Psc has been photometrically observed and studied by several authors. Dezso - 7 -(1945) published 759 photographic observations for R U Psc. These were obtained with the 16 cm astrograph of the Konkoly Observatory from 1937 to 1941. He concluded that R U Psc was undergoing periodic changes in its period, the period of this periodic-ity being ~1080 d . Changes in the shape of the light curve, and a light curve reminiscent of the double-mode R R Lyrae stars in M15 (see Fig. 1 of Dezso's paper, and Nemec 1985b), were also reported. Tremko (1964) published a total of 4603 photoelectric ob-servations of R U Psc, made at the 24-inch, f/5.5 reflector of the Astronomical Institute at Skanalte Pleso, Budapest, through a yellow filter during 52 nights from 1961 to 1964. These data (which have an accuracy of ~ 0m.01) suggested the presence of a secondary Blazhko oscillation of period 28d (based on the periodic brightness changes at mini-mum and maximum light). The photoelectric photometry by Paczynski (1965) gives a very well defined light curve, but since it consists of only three nights observations the data are not useful for the multiple-period problem. Mahra and Sinvhal (1975) found a different solution for the R U Psc period-changing problem. They concluded that the period of the star is on the average increasing at a rate of ~ 1.02 X 1 0 - 6 day per 1000 cycles and that there is a cyclic variation superimposed on this increasing period that has the appearance of a damped oscillation. The periods derived by Mahra and Sinvhal for three different sets of their data are given in Table I. The diversity of opinion on the period behaviour of R U Psc, and the light curve showing large scatter, suggested that a new period analysis should be done on this star. Previous investigations of multiple-period R R Lyrae stars generally have been based on less than ~100 observational data points. The present study of R U Psc is - 8 -TABLE I PERIODS FOR RU PISCIUM Epoch Year Trend Period Source JD 2400000+ 28426-29576 1936-40 decreasing 0.390504 This paper 37513-37998 1961 increasing 0.390318 This paper 38246-38258 1963 decreasing 0.390421 This paper 39055-39472 1966 decreasing 0.390385 Mahra and Sinvhal 39771-39855 1967 increasing 0.390257 Mahra and Sinvhal 40143-40157 1968 0.390385 Mahra and Sinvhal - 9 -based on over 1100 photometric observations by Dezso (1945) and by Tremko (1964). The period determination procedure described by Nemec (1985a,b) was followed. Briefly, periods were calculated using Stellingwerf's (1978) phase dispersion minimization (PDM) technique. Stellingwerf s 0(P) statistic measures the dispersion of the observations about the mean light curve for each trial period P. When 0 is minimized, the best possible light curve in the chosen period search interval is obtained. 1.2.1. Photometry from Dezso (1945) F i g . l a shows a 6 transform using all the Dezso photographic photometry (1937 to 1941, JD 2428426 to JD 2430328), searched over the interval 0^389 and 0d.392. This period search suggests that the primary period equals 0d.39050. The light curve plotted using this period (Fig.2a), shows scatter amounting to a = 0 m . l . To search for a possible secondary period, the Stobie (1970) prewhitening procedure was used to subtract the mean light curve (plotted with the dominant period) from the data. The residuals from the mean light curve were computed and searches for a secondary period were performed. The photometry from Dezso was prewhitened with the period 0^39050 and searched for a second period over the interval 0^520 and 0d.527 (Fig. lb) . A possible period at P n ~ 0d.52334 (marked with an arrow in F i g .lb) gives a period ratio of P\/Po = 0d.746, a typical number for the period ratio for R R Lyrae stars; but the 0 transform does not show the characteristic sidelobes and symmetry often seen in other RRd's . In F ig .2b the light curve for the residuals is plotted using the possible period Po = 0^52334. That shows a weak evidence for the existence of a secondary - 10 -< W .3895 .39 .3905 .391 .3915 - ] — i — i — i — | — I — r — i — i — | — i — r — i — i j i i i — i — | — r — i — i — r r i i i — r .6 R U PSC, DEZSO P H O T O M E T R Y PO = 0.52334 i I i i i i I i i ' ' I ' i i i I i i i (a) JL L • I J I I L .52 .521 .522 .523 .524 PERIOD .525 .526 .527 Fig. 1 (a) — Period search from 0d.389 to 0^ 392 (in steps of 0d.000002), using all the 1936-40 Dezso (1945) data. The primary period, 0^ 39050 is appropriate for this epoch, (b) — Period search of the same data from 0^ 520 to 0d.527 , after prewhitening the original photometry with 0d.39050 . The period step sizes were 0^ 000007 . The possible secondary period, 0d.52334, with 0=0.71, if it were real, would correspond to the ratio of secondary to primary periods, Pi/Po — 0.746 (see Fig. 2 for the corresponding light curves). - 11 -9.5 3 I i i i I i i i I i i i I i i i I i i i I i i i I i i i I i t i - . 4 - . 2 0 .2 .4 .6 .8 1 1.2 PHASE Fig. 2 (a) — Light curve for the period 0d.39050 (see Fig. 1). The scatter about the mean light curve (standard error of a single measurement is 0m.l) suggests that R U Psc is either changing its period, or has a secondary period of the sort seen in RRd stars; (b) — Light curve (using the residuals after prewhitening with P1=0C!39050) plotted with the possible secondary period P0—0d.52334 (see Fig. lb). This period is only marginally significant, and is almost certainly not real. - 12 -component and the period P0 not a true period. = 0 .52334 is only marginally significant and probably 1.2.2. Photometry from Tremko (1964) Period searching the 1961-3 Tremko data (JD 2437513 to JD 2438268) Px = 0d.390318 was derived. This period was used to plot Figs.3a,b and c (light curves using the 1961, 1962 and 1961-3 data respectively). Figs. 3a and 3b suggest that P\ — 0d.390318 is the most appropriate period for the 1961 epoch but not for the 1962 epoch. A clear shift in the phase of maximum light from year to year is seen in Fig. 3c (which uses all the 1961-63 data), indicating that the period is changing. These light curves do not resemble previous R R d star light curves, suggesting that R U Psc is not a double-mode star. Before leaving this large data set, it was of interest to know what the period search would reveal if the data were sampled in a manner similar to the available data for the double-mode R R Lyrae stars in globular clusters and in the Draco dwarf galaxy. To investigate if the 0 transform would, in this case, resemble those of known R R d stars, an attempt was made to simulate the Baade and Swope observation times for stars in the Draco dwarf galaxy (Baade and Swope 1961). For V72 in Draco, for an example, the observations were taken in two different observational periods: 1) 14 nights spread over an interval of 38 days; 2) 18 nights over an interval of 115 days, 262 days later. In an attempt to mimic this time structure the following data set was extracted from the Tremko photometry of R U Psc: 9 nights spread over an interval of 110 days and - 13 -I I I I—I—I—I I I I I I I I I I I I I I I I- I I 1 1 1 I • • • RU PSC, TREMKO PHOTOMETRY, P=0.390318 (a) i i i I i i i I i i i I i i i I i i i I i i i I i i i I i i i -.4 -.2 0 .2 .4 .6 .8 1 1.2 P H A S E Fig. 3 — Light curves plotted with Pi — 0d.390318 (derived from a period search of the 1961-3 Tremko photometry), (a) — for the data from JD 2437513 to JD 2437612 (1961); (b) — for the 1962 data (JD 2437948 to JD 2438059); (c) — for the combined photometry from JD 2437513 to JD 2438268 (1961-3). - 14 -17 nights over an interval of 40 days, 233 days later. The 6 transform for the main period and the search for a secondary period using the residuals (after prewhitening the data with the main period P i = 0m.390434, best period derived using the random selected data) are shown in Figs ,4a and b. These 6 transforms again do not show typical R R d star behaviour and R U Psc does not have the same characteristics as the R R d stars previously identified in the globular clusters M 3 , M15, IC 4499, and in Draco. 1.3. DISCUSSION A N D S U M M A R Y 1.3.1. The Blazhko Variations The primary evidence for the 28^8 Blazhko period for R U Psc (Tremko 1964) is brightness changes at minimum and maximum light. F ig .5 shows six maxima and seven minima in the light curve of R U Psc. Based on the data plotted in this figure, the estimated range in the maximum magnitude is 0™05, and the estimated range in the minimum is 0^08. Fig. 5 also illustrates the cycle-to-cycle changes in the morphology of the light curve that are characteristic of Blazhko and double-mode R R Lyrae stars. The Blazhko-like light variations seen in R U Psc are very common in ab-type R R Lyrae stars, but are generally rare in c-type R R Lyrae stars. According to Szeidl (1975) only two other RRc stars exhibit similar behaviour: (1) B V Aqr has a period P i = 0^364048 and shows evidence for a Blazhko period 11^56 (Tsesevich 1972, unpublished data). The G C V S notes that B V Aqr presents a "complicated Blazhko effect with - 15 -a w ,36 .37 .38 .39 T—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—r R U P S C , T R E M K O SUBSET .41 .42 ~i—i—i—i—i—r («) I P I = 0.390434 (b) i i i i i i i i i I i i i i I i i i i I i i i i 1 i i i i I i i i i I i i i i .51 .52 -53 .54 .55 .56 .57 .58 P E R I O D Fig. 4 (a) — Period search using a subset of the Tremko (1964) data that mimics the observation times of the Baade and Swope (1961) observations for the R R d star V72 in the Draco dwarf galaxy. Search from 0^36 to 0^42, in steps of 0^00051. The most probable period is Px=0d.390434 (0=0.19). (b) — Period search from 0d.50 to 0<*58, in steps of 0d.00078, after prewhitening with 0d.390434. Clearly, there is no evidence for a secondary component. - 16 -b e d « f g Fig. 5 — Light curves for R U Psc (using the Tremko photometry) at maximum and minimum light (a) The top panel shows the following Julian dates: a) 2437565, b) 2437582, c) 2437949, d) 2438053, e) 2438246, f) 2438268. The bottom panel shows: a) 2437589, b) 2437612,c) 2437997, d) 2438020,e) 2438027,f) 2438256, g) 2438258. - 17 -variations in maximum up to three quarters of the amplitude". This is the effect seen in the Draco R R d stars (Nemec 1985a). (2) T V Boo is a metal poor c-type R R Lyrae star with period P i = 0^313. Yubkina (1953) presented light curves for T V Boo which showed cycle-to-cycle variations similar to the variations observed in the light curve of ab-type Blazhko variables. Detre (1965) confirmed that T V Boo is a Blazhko c-type R R Lyrae star, with a secondary period of 33d.5. The changes of the shape of the light curve of R U Psc are small compared to light curves of previously identified Blazhko variables. However, it is clear that there is a range of magnitudes in Fig. 5 that cannot be explained by double periodicity. Since the real time light curves for R U Psc using Tremko's data suggested that the error for a single measurement was larger than the quoted ± 0^01, a reliable statistical analysis of the amplitude and shape variations could not be performed. A more controversial claim is that the 28^8 Blazhko period is also present in the form of period variations (Tremko 1964) that show up as "secondary" oscillations in the O-C diagram (See fig. 1 of Tremko 1964). If reasonable estimates of the errors in the phases at maximum light are made, typically ± 0.03 (phase units), this evidence goes away. 1.3.2. The O-C Diagram To compare the results of the various observers of R U Psc, and to understand the long-term period variations of R U Psc, the O-C diagram shown in F ig .6 was plotted. Tremko's ephemeris, C = 2424057.8450 + 0^3903174 E , was used for each epoch, and - 18 -• 1 1 i j DEZSO (1936-40) 1 J ' 1 1 TREMKO (1957-64) 1 1 1 1 MS (1966-69) x — — — X x x X — * X * X * * — 1 i 1 1 I I I 1 1 , 1 29000 30000 37000 38000 3.9000 40000 JULIAN DATE (2400000+) Fig. 6 — O-C diagram (in phase units) for the times of maximum light. Un-published data from JD 2436000 to 2437300 (1957 to 1960) come from Tremko's fig. 1. A straight line fit through Dezso's data suggest a constant period calculated to be 0^390504. Tremko's data from JD 2437513 to JD 2438418 suggests a non-constant period increase. No cyclic variation in the period changing is seen. the observed times of maximum were derived from the photometry by Dezso (1945), Tremko (1964) and Mahra and Sinvhal (1975). Fig. 6 shows an irregular period change behaviour, suggesting both increasing and decreasing periods. Over the 40 year baseline there is no evidence for the 1080^ period suggested by Dezso. Furthermore, the idea of Mahra and Sinvhal (1975) that R U Psc is evolving towards a state of a stabilized linearly increasing period does not seem to be supported by the photometry. Using all the available photometry for R U Psc, an estimate of its long term period behaviour was attempted. Table 1 gives periods for R U Psc as a function of Julian Date. Considering only the Dezso (1945) data, and assuming a straight line segment for the times of maximum light between JD 2428426 to 2429576, the line shown in Fig . 6 suggests a period 0d.39050, with no period change in this interval. When the Tremko (1964) data (JD 2437513 to JD 2438418) were analysed, periods were derived for two different epochs (see Table 1), suggesting that the period is increasing from 0^390318 to 0^390421 in ~ 800 days. There is no evidence for a steadily increasing period. 1.3.3. Summary Modern period finding techniques were applied to the extensive data sets for R U Psc published by Dezso (1945) and by Tremko (.1964). To investigate the possibility that R U Psc might be a double-mode R R Lyrae star, and to facilitate comparison with previously discovered R R d stars in globular clusters, a period search of a subset of the Tremko data that mimiced the time structure for the R R d stars in the Draco Dwarf Galaxy (Baade and Swope 1961) was also done. - 20 -In an attempt to understand the long-term period behavior of the star, the O-C diagram was plotted using all the available photometry for the star. It is concluded that R U Psc is a star with an irregularly changing period and that it is possibly a Blazhko variable with low-level amplitude changes. Certainly, it is not a double-mode R R Lyrae star of the sort previously identified in globular clusters. -21 -C H A P T E R 2 R A D I A L V E L O C I T I E S OF C - T Y P E R R L Y R A E STARS 2.1. I N T R O D U C T I O N Most studies of the kinematic properties of field R R Lyrae stars suffer from a common problem, namely that the number of stars with known radial velocities is often too small for a satisfactory statistical analysis. Of the ~ 3000 R R Lyraes in the field of the Galaxy, only 260 have known radial velocities (Westpfahl 1988). The present study increases the sample by 20 stars. Radial velocities of R R Lyrae stars are important for the study of a variety of interesting problems. The combination of radial velocities and proper motions allow the determination of R R Lyrae distances and absolute magnitudes through the application of the method of statistical parallax (Van Herk 1965; Hawley et al. 1986). Van Herk used the method of statistical parallax for a sample of 210 R R Lyraes and calculated a mean absolute V magnitude of 0™68. The errors in the calculation of the absolute magnitude are very large mainly owing to the errors in the radial velocities and proper motions. Hawley et al. used the same method for a sample of 159 stars with more accurate radial velocities and proper motions and determined < M y > to be 0.76 ± 0.14 mag. A n attempt was made to investigate the relationship between absolute magnitude and metal abundance. The general trend found was that the brightness decreased with metal abundance but no definite relationship could be defined because of the small size of the samples. The quantitative relation between the absolute magnitude and the metallicity of R R Lyraes is a controversial problem for which no definite answer has yet been found. Such information is essential if R R Lyraes are to be used as accurate distance indicators. Radial velocities of R R Lyrae stars have also become important in the study of other problems. The identification of high-velocity halo R R Lyrae stars can provide a lower limit on the mass of the Galaxy (Hawkins 1983). Radial velocities of remote R R Lyrae stars with known distances can be used to deduce the mass distribution of the Galactic halo (Saha 1985). Multiple radial-velocity measurements over a long time baseline can provide information about the existence of R R Lyraes in binary systems. Discovery of an R R Lyrae star in a binary system would provide a wealth of information; in particular, it would allow an independent estimate to be made of the absolute magnitude of R R Lyrae stars. Most of the radial-velocity surveys of R R Lyrae stars in the field of the Galaxy have focused on ab-type stars. This is mostly because of the large number of ab's compared to c-types. It should also be noted that the c-type R R Lyrae stars are hotter and have broader hydrogen lines than the ab's making the radial-velocity determinations more uncertain. On the other hand, RRc's have lower amplitudes than the RRab's, and they generally have sinusoidal light and radial-velocity curves, which facilitates the determination of the mean radial velocity once a few measurements of the velocity at known phases are made. - 23 -Only 20 c-type field R R Lyrae stars had known radial velocities before this study. In this chapter, velocities are determined for another 20 c-type R R Lyrae stars brighter than 15^0, with declinations > - 1 0 ° , listed in the G C V S (Kholopov 1985). In § 2.2 the observations and the procedures followed for reducing the data are presented. The results, discussion, suggestions of future work and a summary of the chapter are presented in § 2.3. 2.2. OBSERVATIONS A N D R E D U C T I O N S 2.2.1. Spectra Approximately 30 spectra of c-type R R Lyrae stars were taken in two observing runs in June and August 1987. A shectograph (two-channel photon-counting system described by Shectman and Hiltner 1976) was used with the Cassegrain spectrograph on the Dominion Astrophysical Observatory (DAO) 1.8-m telescope. For the nights in June a 600-line m m - 1 grating (No. 2161) was used in first order, giving a reciprocal dispersion of 30 A m m - 1 and a resolution of 4.2 A. The spectral range covered was roughly 3600 A to 4500 A. For the nights in August, a 300-line m m - 1 grating (No. 2131) was used in first order, giving a reciprocal dispersion of 60 A m m - 1 and a resolution of 6.0 A. The spectral range covered was roughly 3500 A to ~ 5400 A. A 2-arcsec slit was used in both runs. The observing procedure is described below. Comparison spectra (using an Fe /Ar lamp) were taken before and after each star exposure. The exposure times for the R R Lyrae stars ranged from 10 min to 50 min, and thus were shorter than 10% of the period of pulsation of the star. Therefore, the stars did not have a large change in radial velocity during the exposures. At least two radial velocity standard stars of spectral types A to K , luminosity class III and V , selected from the Astronomical Almanac, were observed each night. Because the D A O image tube "flops" when the telescope crosses the meridian resulting in a shift in the position of the spectrum on the detector, the radial velocity standards were observed on the east and west sides of the meridian each night. At the end of each night a flat field was taken, which was used to normalize out the pixel-to-pixel variations and the noise pattern of the detector. Two types of flat field exposures were made: observations of a fixed continuum source available on the shectograph ( F L A T 1), and observations of a portable continuum source (a small light bulb) inserted into the spectrograph box ( F L A T 2). F igs .7a and 7b illustrate both kinds of fiat fields taken. 2.2.2. Reduction of the Spectra A l l the reductions were made at the D A O using the I R A F astronomy data reduc-tion package (Tody, 1986). At first the files with the raw data were split into two, corresponding to the upper and lower channels of the shectograph with spectra of either star-sky, comparison-comparison or flat-flat. This was done using the task R S H E C T in the package I M A G E S . After splitting the files the data were reduced in two groups: lower and upper channels, the procedure being the same for both. 0 1000 2000 3000 Pixel Number Fig. 7 — Flat fields, (a) Top Panel — spectrum of a fixed continuum source available on the shectograph ( F L A T 1). (b) Bottom panel — spectrum of a portable continuum source (a small light bulb) inserted into the spectrograph box (FLAT 2). F L A T 2 was found to be more effective than F L A T 1 for the data reduction because the portable source produced more signal in the blue region where most of the significant lines are. The bad column on F L A T 2 occurs at wavelength 3890 A. -26 -The spectra were then trimmed of useless pixels and flattened. F L A T 2, shown in Fig. 7b was found to be more effective than F L A T 1 in reducing the noise in the spectra since there is more signal on the blue region, where most of the important lines are. The division by F L A T 2 was done by fitting a continuum line using the task F L A T 1 D in the package G E N E R I C , and dividing the raw spectra by the fiat using the task I M D I V I D E , also in G E N E R I C . The wavelength calibration of the comparison spectra was then performed. The fitting of a dispersion curve was done using the tasks I D E N T I F Y and R E I D E N T I F Y in the package O N E D S P E C . In the task I D E N T I F Y the pixel number of each unblended high intensity comparison feature was matched to its corresponding wavelength. A Legendre function of order six was used for the fit. A high order polynomial was needed to account for the s-distortion of the shectograph (Shectman and Hiltner 1976). A sample of the typical residuals from the wavelength calibration of a comparison spectrum taken at 60 A m m - 1 , after fitting a sixth order polynomial to 28 identified comparison lines, are shown in Fig.8. The rms residuals of this fit are 0.2 A over the ~ 2000 A spectral window. Special care was taken in setting the correct width of the comparison lines F W I D T H in the task I D E N T I F Y . A correct feature width minimizes errors in the fitting. The remaining comparison spectra of the night were wavelength calibrated using the first calibrated spectrum and the task R E I D E N T I F Y . To perform the wavelength calibration of the stellar spectra the comparison spectra taken just before and just after the star exposure were used. This was done using the task D I S P C O R in the package O N E D S P E C . Sky-subtraction was then performed using - 2 7 -60 o 30 20 10 -10 -20 i + I l l — + + ++ -•f + + ++ + + + + + + + + + f +1 + i i + + i i i 3600 3800 4000 4200 4400 4600 Wavelength (A) Fig. 8 — Typical residuals from the wavelength calibration of a comparison spec-trum, taken at 60 A m m - 1 , after fitting a sixth order polynomial to 28 identified comparison lines. The rms residuals of this fit are 0.2 A, which corresponds to a standard deviation of the mean of ~ 2.0 km s _ 1 for each line. - 28 -I M A R I T H , in the package I M A G E S . A sample of a calibrated spectrum with the sky subtracted is given in F ig .9 . In order to use a cross-correlation routine, the continuum was subtracted from the spectrum. The task C O N T I N U U M in O N E D S P E C was used to fit a continuum line (usually a legendre polynomial) and perform the subtraction. A sample of a rectified stellar spectrum (with the continuum subtracted) is given in Fig.10. 2.2.3 Radial- Velocity Determinations A cross-correlation routine (Tonry and Davis 1979; Welch 1988, unpublished) was used to determine the radial velocities of the R R Lyrae stars. The details of the technique have been outlined by Peterson et al. (1984). Basically a correlation function is plotted against the relative velocity shift between the two spectra. One spectrum is slid over the other in steps, and when the spectra match best a peak is observed in the correlation function. A parabola is then fitted to the peak and the relative geocentric velocity calculated. Most spectra were cross-correlated with the spectra of standard stars observed on the same night and on the same side of the meridian. In a few cases, the cross-correlation was done using a standard star from a different night, since the spectra of late type standards (K and sometimes G) did not cross-correlate well with the spectra of the R R Lyraes, leading to uncertain results. In order to keep the uncertainties as small as possible, the spectra of program stars from one night (night 1) were cross-correlated with standard spectra from a second night - 2 9 -w o 3500 4000 4500 Wavelength (A) 5000 Fig. 9 — Calibrated spectrum (after sky subtraction) for the star V895 Aql . The star has a period of 0^265 and its B magnitude ranges from 13m.5 to 14m.2. The spectrum was obtained using the shectograph, with an exposure time of 960s. - 3 0 -ro 3 O O > • rH -4-3 -TOO h -150 r-3500 4000 4500 5000 Wavelenth (A) Fig. 10 — V895 Aql ; calibrated spectrum after sky and continuum subtraction. - 3 1 -(night 2), according to the following procedure: the velocity for the late spectral type standard star (G or K) observed in night 1 was determined through cross-correlation with an early-spectral type standard (A or F) from night 2. If this value was different from the standard value (given in the Astronomical Almanac 1987) by ± 5 km s _ 1 or less, the early spectral type standard from night 2 was considered acceptable for cross-correlation with the program stars in night 1. In this ± 5 km s 1 instrumental error was added to the total error involved in the determination of the velocities (see section 2.3.2). 2.3. R E S U L T S A N D DISCUSSION Table II lists the radial velocity standard stars observed. Columns 2 and 3 give the HD or B D numbers and the Julian date of the observations. A n "e" or "w" in column 4 indicates if the star was observed on the east or west side of the meridian. In column 5 the spectral types are given. Column 6 gives the standard velocities for the stars given by the Astronomical Almanac (1987). Column 7 lists the heliocentric corrections. The corrections were determined using the program R E D T O S U N (Fletcher 1987, unpublished) at the D A O . Table III summarizes the results for the 21 program stars that were observed. Four independent measurements were made for the stars K N Per and V Z Peg, two independent measurements were made for seven stars and a single measurement was made for the other 12 stars. Column 1 lists the stars' identification. Columns 2 and 3 list the Galactic longitude and latitude (1 and b). Column 4 lists the heliocentric - 32 -TABLE II STANDARD STARS USED FOR CROSS-CORRELATION N Star Hel.JD Side of Spectral type Vrad Hel.corr. (2440000+) meridian (Km/s) (Km/s) W. (2) (3) (4) (5) (6) (7) 1 HD 12029 7037.9808 e K2III 38.6+0.5 24.66 2 HD 23169 7036.9262 e G2V 13.3+0.2 29.34 3 7040.0107 e 28.99 4 HD 82681 6976.7430 w A -60.0+4.0 -25.79 5 6978.7939 w -25.78 6 HD 149803 6974.8608 w F7V - 7.6+0.4 -10.95 7 6975.7682 w -11.04 8 7036.7349 w -18.65 9 BD 283202 7035.7195 e F7V -36.6+0.5 -10.14 10 7035.9121 w -10.45 11 7038.6805 e -10.89 12 7038.7697 w -11.06 13 7039.7564 w -11.34 - 33 -TABLE III RADIAL VELOCITIES FOR c-TYPE RR LYRAE STARS Name 1 b Hel.J.D. Phase <j> Side of Std. Hel.corr. (2440000+) (days) meridian (km/s) (km/s) (1) (2) (3) (4) (5) (6) (7) (8) (9) V476 Aql . 39.0 3.8 7037.8308 0.02 w ( l ) 1 -28.6 -20.7 V895 Aql . 44.4 -11.9 7039.8237 0.17 w (13) 79.1 -16.5 AE Boo .. 18.0 61.3 6975.8346 0.95a w ( 7) 154.1 -22.7 6976.7704 0.92° w ( 4) 118.9 -22.8 V508 Cyg 84.8 4.0 7036.8956 0.64 w ( 8) -17.8 -0.6 7037.7909 0.94 w (12)c -53.4 -0.7 V789 Cyg 63.1 7.1 7039.8459 0.10 w (13) 48.8 -12.1 6974.9319 0.13 w ( 6) -37.1 7.1 V791 Cyg 65.4 6.8 7035.8728 0.86 w (10) -83.7 -10.0 V997 Cyg 85.9 13.4 7037.8692 0.65 w (12)c 15.5 -1.9 7038.8266 0.83 w (12) 53.1 0.2 V1719 Cyg 91.0 2.6 7035.7577 0.50" e ( 9) 33.5 3.1 7036.7699 0.29 e ( 2) 40.7 2.9 CE Del .. 53.2 -15.0 6975.9407 0.78 w ( 7) -87.5 14.2 CH Del .. 59.1 -11.4 6978.8760 0.45 e ( 5)» -124.8 13.2 FP Del . . . 56.5 -18.9 7039.8925 0.36 w (13) -102.6 -10.3 II Del . . . . 64.6 -15.4 7038.9005 0.07 w (12) -140.4 -7.2 IT Her . . . 55.2 12.4 6974.8952 0.47 w ( 6) -72.1 3.1 LW Her .. 49.4 25.8 6976.9294 0.85 w ( 4) 20.2 -5.0 DE Lac .. 92.9 -12.4 6978.9070 0.83a e (5) ' -12.8 19.2 V1017 Oph 8.4 30.9 6976.8424 0.50° w ( 4) 112.6 -16.2 VZ Peg .. 103.6 -35.3 7035.7954 0.61 e ( 9) -185.9 14.1 7035.9893 0.24 w (10) -184.5 13.7 7036.8673 0.10 e ( 2) -193.4 13.5 7039.9423 0.14 w (13) -232.5 12.1 KN Per .. 151.1 -13.1 7035.9513 0.78 e ( 9) -17.0 27.3 7036.9512 0.09 e ( 2) -20.1 27.2 7038.0015 0.52 e ( l l ) c -14.0 27.1 7039.9665 0.05 e ( 3) -22.2 27.0 KVPer .. 131.9 -4.3 7036.9760 0.16 e ( 2) 84.5 21.2 YZ Tau .. 166.8 -23.2 7038.9821 0.03 e (11) 57.6 29.3 7039.9851 0.47 e ( 3) 94.5 29.2 SX UMa . 113.2 60.2 6975.7958 0.47a w ( 7) -125.8 -14.7 6978.8276 0.34 w ( 5) -79.4 -14.3 - 34 -TABLE III (continued) RADIAL VELOCITIES FOR c-TYPE RR LYRAE STARS Name Vr(<j>) c <Vr> E(B-V) AB <B> ( m - M)0 d (km/s) (km/s) (km/s) (mag.) (mag.) (mag.) (mag.) (kpc) (10) (11) (12) (13) (14) (15) (16) (17) V476 Aql . -35 46 V895 Aql . 37 7 AE Boo .. 135 9 62 3 V508 Cyg -7 13 -80 7 V789 Cyg 12 5 -27 5 V791 Cyg -120 13 V997 Cyg -12 14 28 12 V1719 Cyg 10 5 28 13 CE Del . . -70 4 CH Del . . -146 16 FP Del . . . -138 18 II Del . . . . -173 14 IT Her . . . -66 12 LWHer . . -19 5 DE Lac .. -28 15 V1017 Oph 62 9 VZ Peg .. -198 12 -197 17 -196 20 -246 22 KN Per . . -16 7 -9 13 -13 11 -11 14 KVPer . . 90 18 YZTau .. 61 14 108 16 SXUMa . -137 9 -128 4 -22 - -34 0.18 0.72 146 0.00 0.00 72 7 — / -69 18 - --25 -112 - --12 0.09 0.36 35 4 - -15 -65 0.18 0.72 -154 0.15 0.60 -149 0.09 0.36 -165 0.12 0.48 -73 0.24 0.96 -11 0.09 0.36 -21 0.24 0.96 56 0.18 0.72 -199 0.03 0.12 -13 0.15 0.60 89 72 0.12 0.48 101 -144 0.00 0.00 -139 13.75 13.0r 3.9r 13.85 12.3 2.9 10.66 9.9 0.9 13.55 12.8r 3.5r 13.50 12.7r 3.5r 13.45 12.7r 3.4r 14.50 13.3 4.7 14.50 13.7r 5.5r 8.14 - -13.55 12.0 2.5 13.20 11.8 2.3 14.15 13.0 4.0 14.65 13.4 4.7 13.10 11.3 1.9 13.20 12.0 2.6 10.75 9.0d 0.Qd 14.60 13.1 4.1 11.90 11.0 1.6 11.50 10.1 1.0 14.05 13.3r 4.5r 13.65 12.4 3.0 10.89 10.1 1.0 a Accurate phase; * Std. star not observed in the same side of the meridian as the program star; c Std. star not observed in the same night as the program star; d Assumed to be an RR Lyrae; r Not corrected for reddening. - 35 -Julian dates at mid-exposure. Column 5 gives the phases (in days) at which the stars were observed, calculated using the times of maximum light given by the G C V S or by Banachiewicz (1987), the latter for the stars brighter than 12™0. Phase 0.0 corresponds to maximum light or minimum velocity. Accurate phases are known for only ~ 25% of the stars (so indicated in Table III). For the other stars, the ephemerides given by the G C V S are old, and it is likely that the phases listed are very different from the present-day phases due to period changes. Nevertheless, since this was all that was available, the phases were calculated in order to determine the mean velocities given in column 12. A n "e" or "w" in column 6 indicates that the star was observed either to the "east" or to the "west" side of the meridian. Column 7 lists the standard stars which were used for the cross-correlation (numbers refer to column 1 of Table II). Columns 8 and 9 list the relative velocities of the program stars with respect to the standard stars and the heliocentric corrections. In column 10 the radial velocities reduced to the Sun at the phases given in column 5 are listed. These values were obtained by adding columns 8 and 9 of this table with the velocity of the standards given in column 6 of Table II and subtracting the heliocentric corrections given in column 7 of Table II. The estimated errors in the determination of the velocity at a given phase are listed in column 11. Column 12 gives the final mean velocities calculated as described in § 2.3.1 below. Detailed explanation about how the uncertainties were estimated is given in § 2.3.2 below. Columns 13 to 17 list, respectively, the E(B-V) color excess, the interstellar extinction AB, the mean apparent magnitude given by the average of the maximum and minimum magnitudes given by the G C V S , the distance modulus - 36 -corrected by reddening when the reddening is available, and the distance d in kpc. Explanation about how these quantities were derived is given in § 2.3.3. The positions of the stars in galactic coordinates is shown in F ig .11 . Positive and negative velocities are indicated by plus signs and open circles respectively. The two high latitude stars are A E Boo and SX U M a . 2.3.1. Mean Radial Velocities A standard radial-velocity curve was determined using the set of observations for T Sex given by Barnes et al. (1988). This velocity curve was chosen as standard because there is not another radial-velocity curve for an RRc in the literature with good phase coverage. The amplitude of the radial-velocity curve for T Sex as read from Fig. 14 of Barnes et al. (1988) is 26 km s~l. In order to determine the mean velocities from just one or two velocity measurements for the program stars, we assumed that the shapes and amplitudes of the radial-velocity curves were the same as for T Sex. Since most of the c-type R R Lyrae stars have sinusoidal curves, the first assumption does not introduce large uncertainties. The uncertainties due to the assumed amplitude are discussed below. As an example of how the mean velocities were determined, the calculation for V476 Aql is described. A radial velocity of -35 km s _ 1 at phase 0^02 was determined for this star using cross-correlation techniques. Since phase 0.0 was assumed to be of maximum light and minimum velocity, V476 Aql was observed very close to its minimum velocity phase. Therefore, 13 km s - 1 (half of the amplitude of the radial - 3 7 -NGP Fig. 11 — Galactic positions of the RR Lyrae stars observed. Latitude and longitude are as indicated. The plus signs represent stars with positive radial velocities and the circles represent stars with negative radial velocities. velocity of T Sex) was added to -35 km s 1 to correct from minimum to mean velocity. However, the value of 26 km s _ 1 is probably not the correct amplitude for V476 Aql . This star has a light amplitude of 0^45 compared to 0m.25 for T Sex. It is expected then that the amplitude of its radial-velocity curve should also be larger than for T Sex. Since there are only a few radial-velocity curves for c-type R R Lyrae stars available, it is hard to estimate the error introduced by the assumed amplitude. Hawley (1985) concluded that the assumed amplitude of the standard radial-velocity curve should not have a large effect on the mean velocities. When two observations were available for one star, a mean velocity was estimated from each observation separately. These values are also listed in column 12 of Table III. The final mean is just the average of the two values. The mean velocities determined for A E Boo, V508 Cyg and V789 Cyg from two different spectra are discrepant. Both spectra for A E Boo and V789 Cyg were of reasonable signal-to-noise ratio (< S/N >~ 20 for A E Boo, and ~ 15 for V789 Cyg) and were cross-correlated with spectra of standard stars taken on the same night and at the same side of the meridian. The spectrum of V508 Cyg taken on the JD 2447036.8956 was of low signal-to-noise ratio (< S/N >~5) and the velocity derived was more uncertain. The spectrum taken on the JD 2447037.7909 presents a good signal-to-noise ratio (< S/N >~18), but it was cross-correlated with a standard star spectrum from a different night. For the other four stars, V997 Cyg, V1719 Cyg, Y Z Tau and SX Uma, for which two measurements of the velocities are available, the mean velocities agree within the errors. For the star V Z Peg, four measurements are available. The measurement with the largest error is - 3 9 -very discrepant and the mean was determined using only the three other points. For the star K N Per, for which four measurements of the velocity well distributed in phase are available, the mean was estimated by eye. The mean is -13 km s - 1 with a 10 km s _ 1 amplitude. A histogram in Fig .12 shows the distribution of the velocities. Star V1719 Cyg is a dwarf Cepheid (Mantegazza and Poretti 1986) and it was not included in this histogram. The mean radial velocity for the 20 R R Lyrae stars is -39.0 km s _ 1 with a standard deviation of the mean of 91.5 km s _ 1 (i.e. the sample of R R Lyraes observed is dominated by stars with negative velocities). Unfortunately proper motion information is still not available for any of the stars in this study and determinations of U , V , W space velocities are not possible. With the exception of the stars V1719 Cyg, SX Uma and Y Z Tau, all the other R R Lyrae stars listed in table III are included in the Lick Northern Proper Motion program (Klemola et al. 1987 and Hanson 1988) and proper motion for these stars will be available to the astronomical community in a few years. 2.3.2. Uncertainties in the Velocities There are three main sources of errors associated with the calculation of the veloc-ity at a given phase: instrumental errors, errors due to the cross-correlation technique, and errors due to the wavelength calibration. One of the major limitations in the accuracy of the results is imposed by the instruments used. The flexure of the spectrograph (shift of the spectra for different positions of the telescope), and "flopping" of the D A O image tube when crossing the - 4 0 -i r "i r ~i 1 r ~i 1 r N C-TYPE FIELD RR LYRAE STARS J I L J L J I L -200 -100 0 Radial Velocities 100 J L 200 Fig. 12 — Histogram showing the distribution of velocities for the c-type R R Lyrae stars observed. Six of the stars have positive velocities and 14 have negative velocities. The mean velocity is -39.0 km/s with a standard deviation from the mean of 91.5 km/s. - 41 -meridian introduce large uncertainties in the results. To minimize the problem of flexure of the spectrograph, comparison spectra were taken just before and after each star exposure, without moving the telescope while the three spectra were accumulating. To account for the problem of the "flopping" of the image tube, stars observed on each side of the meridian were treated independently, meaning that stars observed on the east (west) were cross-correlated with standard stars also on the east (west). For nights where only late spectral type standards were observed, the spectra of the program stars had to be cross-correlated with standard star spectra from another night. In these cases (indicated in Table III), a typical uncertainty of ±5 km s - 1 was added to take into account of the instabilities of the instrumental system. In a few cases, spectra of stars taken at different sides of the meridian had to be cross-correlated. For those stars (indicated in Table III), the measurements are more uncertain and an instrumental error of typically ±10 km s _ 1 was introduced (This error was estimated from the cross-correlation of spectra of two standards observed in the same night, one on each side of the meridian). The errors associated with the cross-correlation technique are determined by the line shape and by the counting statistics of the line strength for the two spectra being correlated. At low signal-to-noise only the broad hydrogen lines and the calcium lines in the late-spectral-type R R Lyrae stars are strong enough to measure; this makes the velocity determinations uncertain. The uncertainty in the determination is quantita-tively evaluated from r, the empirical ratio of the correlation peak height to that of the typical noise peak. This error was calculated using equation (24) from Tonry and - 4 2 -Davis (1979). The rms residual of the pixel to wavelength conversion is small compared to the other source of errors (see fig. 7). The total error for one velocity measurement is the sum in quadrature of the errors due to the instability of the instrumental system, to the cross-correlation technique and to the wavelength calibration. These are listed in column 11 of Table III. The major source of error for those stars, however, is the derivation of the mean radial velocities, since for most of the stars only one measurement is available, the phases are not accurate and the amplitude of the radial-velocity curves are not known (for the few RRc's for which good coverage is available, the amplitudes are typically 20 to 50 km s _ 1 ) . The error involved in the derivation of the mean velocity of the R R Lyrae stars with reliable ephemeris is estimated to be of the order of ±15 km s _ 1 . In the case of K N Per, for which four measurements of the velocity are available, the uncertainty in the derivation of the mean is probably less than ± 10 km s _ 1 . 2.3.3. Determination of the Distances The E ( B - V ) color excesses listed in column 13 of Table III were derived from the contour maps of Burstein and Heiles (1982) for stars with galactic latitude b > 10°. The relative values of these reddenings are estimated by Burstein and Heiles to be accurate to about ± 10%. A n assumed ratio of AB to E ( B - V ) of 4.0 (Mihalas and Binney 1981) was used to calculate the values of the extinction coefficient As listed in column 14 of the same table. To calculate the distance modulus an absolute mean B - 4 3 -magnitude of +0™8 was assumed for all the c-type R R Lyrae stars. For the stars with b < 10° no reddenings were available and the distance moduli were not corrected for reddening. The distance d (kpc) was determined using the average of the minimum and maximum apparent magnitudes given by the G C V S . The uncertainties on the distance determinations, corrected for reddenings, are on the order of ± 20% 2.3.4. Notes on Individual Stars Several of the stars in this study deserve special mention: V 5 0 8 C y g - The spectrum did not resemble a spectrum of an R R Lyrae star. The G-band is pronounced and the hydrogen lines are still present, hinting it is a late F or an early G star. If the ephemeris for V508 is correct, the star was observed close to its hottest phase (<p = 0.94), which suggests that either the chart used (Lehnhausen 1957) was incorrect or this c-type R R Lyrae star is uncommonly cooler than the others. V508 Cyg (P=0C?3898) could also be a short period, b-type R R Lyrae star. A weak argument against this is its sinusoidal light curve (however short period b-type R R Lyrae stars tend to have symmetrical light curves). On the other hand, if it really is a first-overtone pulsator, it is a peculiar object in the sense that it does not have the appropriate temperature for a horizontal branch star. It could be that V508 Cyg is a star evolving off the horizontal branch, towards the asymptotic giant branch, in which case it would be cooler than a normal c-type. The only information available on V508 Cyg is a light curve given by Hoffmeister (1949). The spectrum for the star is shown in F ig .13 . - 4 4 -Fig. 13 — Spectrum of V508 Cyg. It does not resemble the spectrum of an R R Lyrae star. -45 -V 1 7 1 9 C y g - This star was included in the observing list since it is classified as an RRc in the G C V S (Kholopov 1985). However, according to Mantegazza and Poretti (1986) it is a double-mode 6 Scuti star with periods Pi=0c*267298 and P2=0<*2138. D E Lac - This star (P=0<?254) is classified as an RRc in the G C V S (Kholopov 1985), but Paczynski (1965) classifies it as a long period dwarf Cepheid. Most RRc stars present a pre-maximum hump on the light curve before maximum light. No such feature is seen on the light curve for D E Lac (Paczynski 1965). Like D E Lac, there are many other variables with periods between 0^2 and 0^3 and sinusoidal light curves, for which the classification type is not certain. Suggestions of future work in this area are discussed in section 2.3.5. K N P e r - F ig .14 shows the radial-velocity curve for K N Per. A typical error bar of ± 11 km s _ 1 is also plotted. Despite the large errors, the shape of the radial velocity curve is as expected. There is no light curve published for K N Per. The mean systemic velocity is -13 km s _ 1 with an amplitude of ~ 10 km s - 1 . S X T J M a - Joy (1938) has determined the radial velocity for SX U M a at Julian Dates 2424980.851 and 2426460.896 to be -79.5 and -126.6 respectively. These val-ues are lower than the two determinations of -137.0 and -128.2 made in this study (see Table III) but they agree fairly well considering the large errors involved in both determinations. 2.3.5. Future Work and Summary Field c-type R R Lyrae stars have periods in the range ~ 0d.2 to ~ 0^4, amplitudes - 4 6 -> -10 -20 "i r r "i 1 r \ i r RADIAL VELOCITY FOR K N P e r - P=0.433224 .5 PHASE Fig. 14 - Radial velocity curve for the star K N Per. The time of zero phase has arbitrarily been set at 2400000.0. The mean error on a single measurement, as indicated by the error bar, is ~ 11 km/s. - 4 7 -from ~ 0™3 to ~ 1™0 and [Fe/H] ~ -0.7 to ~ -2.0. These stars are poorly studied despite their short periods and brightness (many are brighter than 12™0). Most of them do not have precisely determined periods and light curves based on good photoelectric data are available just for a few bright RRc's . There were only 20 stars with known velocities before this study. In this chapter, first-time radial velocities were obtained for another 20 RRc's . However, better phase coverage is needed to provide more accurate values of mean radial velocities. In order to enhance our understanding of field c-type R R Lyrae stars and to fill these and other gaps in our knowledge, I would like to suggest these projects that I think would be very interesting and worthwhile: 1) The list of radial velocities of c-type R R Lyrae stars started in this chapter is incomplete. A worthwhile project would be to complete this list and then to combine the radial-velocity data with proper motion information to derive absolute magnitudes for a larger sample of c-type R R Lyrae stars. This could be done using the method of statistical parallax, as was done by Hawley et al. (1986) for ab-type R R Lyrae stars. 2) Radial-velocity curves for c-type R R Lyrae stars need to be obtained, preferably using a radial-velocity scanner (for the moderate to high metallicity stars), since first estimates of the velocities are now available. With a few stars with good phase coverage, one could investigate the relationship between the amplitude of the light curve and the amplitude of the radial-velocity curve for these stars (i.e. calibrate the Aphotometric-amplitude - A velocity-amplitude relation). - 4 8 -3) The spectral classification of the short-period (periods between 0d.2 and 0^3) c-type R R Lyrae stars needs further work. One of the main objectives of such a project would be to clearly differentiate between RRc's (that are giants) and dwarf Cepheids, which have periods in the same range as those of the RRc stars but are of lower luminosity. 4) Another project would be to investigate the existence of radial second-overtone pulsators among R R Lyrae stars. It has been suggested that if these stars exist, they should have approximately the same period and amplitude ranges as the short period low amplitude RRc's , but that they should be fainter (Stothers 1987; Stellingwerf et al. 1987) and may have unusual light curves. 5) One could also determine the frequency of c-type R R Lyrae stars that present pre-maximum humps in their light curves and investigate the value of using this feature in distinguishing RRc's from dwarf Cepheids and second overtone pulsators. 6) The c-type R R Lyrae stars B V Aqr and T V Boo (< B > ~ 10mA and llm.2 respectively) are in need of good photometric data. These stars are known to present light curves with a large scatter and certainly deserve a new period analysis of the sort done for R U Psc in chapter 1. In particular, one should check to see if these stars are either double-mode pulsators or Blazhko variables. In summary, in this chapter, radial-velocity determinations were made for 20 c-type R R Lyrae stars whose velocities were previously unknown. Many of the stars in this study are being observed again using a C C D camera on the 1.8-m telescope at D A O . A complete report on all the velocities is being readied for publication (Oliveira, Nemec and Welch 1988, in preparation). - 50 -C H A P T E R 3 C C D P H O T O M E T R I C S T U D Y OF S E V E N V A R I A B L E STARS IN T H E U R S A M I N O R D W A R F G A L A X Y 3.1. I N T R O D U C T I O N Dwarf spheroidal galaxies are interesting and important objects in that they are systems where old and young populations of stars coexist. The Ursa Minor and Draco dwarf spheroidal galaxies have the lowest luminosities and smallest masses of the Local Group spheroidals; hence they are most similar to globular clusters in these respects. On the other hand, these two dwarf galaxies possess many of the characteristics common to most of the spheroidals of the Local Group which distinguish them from globular clusters. Only one globular cluster is known to possess an anomalous Cepheid (see section 3.4.4): N G C 5466 (Zinn and Dahn, 1976; Zinn and King 1982). Anomalous Cepheids have been found in all the spheroidals where they were searched for: Draco, Ursa Minor, Leo I, Leo II, Sculptor and Fornax (Swope 1968, Zinn and Searle 1976, Hodge and Wright 1978, Light et al. 1986, and NWO) . Except for w Cen (Rodgers et al. 1979, and Cohen 1981) and M22 (Hesser et al. 1977, and Norris and Freeman 1983), globular clusters do not show nearly so large a range in internal metallicity as do dwarf spheroidals. Among the dwarf spheroidals, Ursa Minor is somewhat different in that it possesses only two known carbon stars, while the others have large numbers (Aaronson et al. - 5 1 -1983 and Aaronson and Mould 1985). It is also the only dwarf galaxy to possess a blue horizontal branch, which is commensurate with the low metal abundances determined by Zinn (1981), Stetson (1984) and Aaronson and Mould (1985). The Ursa Minor dwarf spheroidal galaxy was discovered by Wilson (1955), from a search on the original plates of the Palomar Sky Survey. The first studies were done by van Agt (1967, 1968). Analysing 148 plates taken at the prime focus of the 5-m Hale telescope (1953 to 1958), he discovered and studied 92 variables, and constructed the first colour-magnitude diagram (CMD) for the system. Kholopov (1971) reanalysed van Agt's data and calculated improved periods for ten variables. Among the recent studies of Ursa Minor, a new colour-magnitude diagram from C C D data was constructed by Olszewski and Aaronson (1985; hereafter OA); Cudworth et al. (1986) studied proper motions, probabilities of memberships and presented bright star photometry; and, an extensive study of the system's variable stars has been sub-mitted for publication by Nemec, Wehlau and Mendes de Oliveira (1988). In this chapter, new C C D data is combined with all the available data to get new periods for five c-type R R Lyrae stars, one RRab and one anomalous Cepheid in Ursa Minor. Accurate information on magnitudes and colours for these stars is obtained, which allows a new distance modulus to be derived using the c-type R R Lyrae stars at the blue edge of the instability strip. Also, the existence of double-mode R R Lyrae stars and second-overtone pulsators in the system is investigated. In § 3.2 the observations, the procedures followed for reducing the data, and the results are presented. In § 3.3 details of the period searches and light curves for the stars are given. In § 3.4 a CMD for the Ursa Minor spheroidal galaxy is shown, a new distance determination is made and discussions concerning RRc's, double-mode RR Lyraes, anomalous Cepheids and second-overtone pulsators are presented. The results of the chapter are summarized in § 3.5. 3.2. OBSERVATIONS AND REDUCTIONS 3.2.1. The C C D Frames The data for the present study consist of 38 CCD frames taken by Dr. J.M. Nemec on 4 consecutive nights in 1984, May 31/June 1 to June 3/4, using the KPNO No. 1, 36 inch (0.9 m) telescope with the CCD Direct Imaging Camera, f/13.5 (hereafter KP36 CCD data). Table I V lists the 31 B and 7 V frames. The universal time, hour angle and air mass are the values at mid-exposure. The frames cover an area of 2*5 x 4'.1, centered on R.A. 15h 8m.2 (1950.0) and Dec. 67° 24' (1950.0). This field was chosen to include the seven variables: V55, V57, V58, V59, V83, V95 and V97 (van Agt 1967), five of which are long-period c-type RR Lyrae stars. According to a previous analysis of the Van Agt photographic data (Nemec 1984), several of these were believed to be possible double-mode pulsators. During the four nights, the frames were placed in slightly different positions so that all the stars indicated in Fig.15 were observed and measured at least once. Fig. 15 is a composite photograph of the second and last B frames of night 2 and the fourth frame of night 4. The frames were flattened and trimmed of bad columns at the Image Processing TABLE IV CCD FRAMES OF THE URSA MINOR DWARF G A L A X Y HJD Filter Exp. Time U.T. H.A. Air Mass 2445000+ (min.) (mid) (mid) (mid) 852.7944 B 20 7 f c04 m 1 h 0 5 m W 1.25 852.8194 V 20 7 h 4 0 m l h 4 1 m W 1.28 852.8354 B 20 8 h 0 3 m 2 h04 mW 1.30 852.8542 V 30 &h30m 2 h31 mW 1.34 852.8750 B 20 9h0Qm 3 f c01 mW 1.39 852.8944 V 30 9h28m 3 h29 mW 1.45 852.9174 V 30 1 0 h 0 1 m 4 h02 mW 1.54 853.7548 B 20 6h07m 0'l12mW 1.23 853.8055 B 20 7h20m l h 2 5 m W 1.26 853.8249 B 20 7h48m l h 5 3 m W 1.29 853.8450 B 20_ 8 h 1 7 m 2 h22 mW 1.32 853.8624 V 25 8 h 4 2 m 2 h47 mW 1.36 853.8860 B 20 9 h 1 6 m 3 h21 r oW 1.43 853.8999 V 30 9h36m 3 h41 mW 1.48 853.9221 B 30 lo^os™ 4 A13 mW 1.57 853.9423 V 25 10h37m 4 h 4 3 m W 1.68 854.7478 B 20 5h57m 0 A 0 6 m W 1.23 854.7673 B 30 6h25m 0 h34 mW 1.23 854.7895 B 30 Qh57m l h 0 6 m W 1.24 854.8103 B 30 7h27m l f c 3 6 m W 1.27 854.8325 B 30 7h59m 2 h08 mW 1.30 854.8548 B 30 8 f c31 m 2 h40 mW 1.35 854.8728 B 20 g h 5 7 m 3 / l06 mW 1.40 854.8874 B 20 9 h 1 8 m 3 h27 mW 1.44 854.9062 B 30 9 h 4 5 m 3 f c54 mW 1.51 854.9284 B 30 1 0 h 1 7 m 4 h26 mW 1.61 854.9464 B 20 1 0 h 4 3 m 4h52mW 1.71 854.9610 B 20 l l h 0 4 m 5 h14 mW 1.80 855.6735 B 25 4h10m l h 3 8 m E 1.28 855.7055 B 30 4 h 5 6 m O h52 r oE 1.24 855.7291 B 30 5 f c30 m 0 h 1 7 m E 1.23 855.7562 B 30 6 h 0 9 m 0*22 mW 1.23 855.7770 B 30 6 h 3 9 m 0 h52 mW 1.24 855.8645 B 30 8h45m 2 h58 mW 1.38 855.8860 B 30 9h16m 3 h29 mW 1.45 855.9138 B 30 9h5Qm 4 h09 mW 1.56 855.9346 B 30 10 h26 m 4h39mW 1.66 855.9555 B 30 I O ^ " 1 5 h09 mW 1.78 - 54 -Laboratory at K P N O , following the observing run. Instrumental magnitudes for all the stars were measured by Nemec (25 frames) and Oliveira (6 frames) using D A O P H O T (Stetson 1987). Average point-spread functions were determined for each frame. Since the frames were sparsely populated, P E A K instead of an N S T A R photometry was performed. 3.2.2. Calibration of the Frames The calibration to the Johnson system was done using stars from O A measured on the C C D frames. A n independent calibration was attempted using six standards in M92 (Christian et al. 1985) and five equatorial standards from Landolt (1983). Table V contains the photometry for the O A stars used to transform the instru-mental to standard magnitudes. Column 1 gives the star's designation from this study (identified in Fig . 15). Columns 2 and 3 list magnitudes from OA used to calibrate the V and B C C D frames of nights 1 and 2 to the Johnson system (assuming that OA magnitudes are on the Johnson system). Only B frames were taken on nights 3 and 4 and the calibration of these frames was done using average magnitudes derived from the well measured stars from nights 1 and 2 (standard deviation of the mean, s.d.m. < 0™015). These mean magnitudes are listed in column 4 of table V , under B(l ,2) . Columns 5 and 6 list the number of measurements used to calculate B(l,2) and the standard deviation of the mean. Using results from the first two nights to calibrate the last nights observations, the calibration curves were smoothed and better results thus achieved. - 56 -TABLE V PHOTOMETRY FOR THE CALIBRATION STARS No. V(OA) B(OA) 5(1,2) n a (mag.) (mag.) (mag.) (mag.) (1) (2) (3) (4) (5) (6) 8 19.82 — - - -9 20.93 - - - -11 20.04 - - - -19 21.31 - - - -20 - - 20.10 9 0.014 23 19.44 20.20 -• - -25 19.11 19.86 19.87 9 0.010 28 18.87 19.47 - - -30 19.59 20.05 - - -32 16.88 18.38 18.33 9 0.005 33 - - 19.79 9 0.011 36 18.88 19.72 19.72 8 0.008 37 20.09 20.83 20.79 6 0.015 38 18.57 19.44 19.45 9 0.009 43 19.11 19.96 19.93 9 0.011 44 19.83 21.26 - - -45 19.70 21.33 - -48 19.48 20.20 20.20 9 0.013 49 17.01 18.24 18.28 9 0.005 55 - - 20.32 9 0.013 57 20.52 21.47 - - -58 20.31 21.00 - - -59 20.37 20.97 - - -67 20.28 21.00 - - -77 - - 20.10 7 0.014 78 - - 18.78 8 0.013 - 57 -Plots of BOA versus Bin3t (calibration curves) were made for each frame and a least squares fit using R E T I C E N T (Pritchet et al. 1982) was performed, weighting the instrumental B magnitudes by their standard error given by D A O P H O T . First, second and third order polynomials were tried in order to get the best fit. F ig .16 shows two representative curves. A n average of 16 O A stars were used to calibrate the B frames for nights 1 and 2, and 13 stars were used for nights 3 and 4. Stars 11 and 39 were initially used as calibration stars, but because they did not fit the calibration curves, they were excluded and treated as program stars. The calibration of the V frames was done in the same way as for the B ones. A n average of 18 stars were used. Star 44 was systematically off the calibration curves and therefore not used as a calibration star. A n independent calibration of the C C D frames was also attempted. Stars A , A A , 9, 10, 25 and 26 in M92 (Christian et al. 1985) and the equatorial standards 104-306, 118246, 105-405, 106-700 and 2-2711 from Landolt (1983) were used as calibration stars. Standard extinction coefficients for Ki t t Peak were used: ks-v = 0.105(±0.063), ky = 0.186(±0.041) (Bushouse, 1985) and only observations made at low air masses (X < 1.35) were compared. The colour term correction and zero point were derived, but with large uncertainties. F ig .17a shows a plot of v — V — fcyX against B - V . The slope and y intercept of the best first order fit gives the following transformation equation: V = v - 3.60(±0.02) - 0.05(±0.03)(5 — V) — 0.19(±0.04)X - 58 -Fig. 16 — Two examples of weighted least square fits, used for calibration of the instrumental V and B magnitudes to the standard system. The OA photometry for the standard stars is given in Table V . - 5 9 -Fig. 17 _ Standard stars transformations. The lines are the best fit to the data as described in the text. In b) only stars for which accurate B and V photometry is available are plotted. - 60 -In F ig .17b , (B-V) is plotted against (b — v) — fc^-vX. The best fit gives the equation: B - V = 1.30(±0.06)(& -v- 0.11(±0.06)X) + 0.718(±0.050) , where b and v are magnitudes in the instrumental system and V and B are standard magnitudes. Using these two equations, standard magnitudes and colours were derived for ten bright stars and compared with the results obtained from the calibration using OA's photometry. The results are the same within ± 0™1. This discordance is mainly due to errors in the colour term, zero point, and to the uncertainty in estimating the correction from a 3-pixel aperture magnitude to total magnitude for the program stars (magnitudes were derived using the P E A K program in D A O P H O T , normalized to a three pixel aperture). The correction is usually derived from multiple aperture photometry of bright stars. A plot of the P H O T magnitude, as a function of aperture radius, for the brightest stars in the frames shows that the magnitude becomes brighter up to a limiting radius that contains all the light from the star. The correction is then the difference between the magnitude at the limiting radius and at the radius to which the original peak photometry was normalized (in this case, 3 pixel aperture). There were only three bright stars in most of the Ursa Minor V frames, often one close to a bad column and two close to the edge of the frame. For this reason, corrections were calculated using faint stars, introducing a typical error of ~ 0™05 (this error was estimated comparing corrections derived using bright and faint stars in one of the frames where the bad columns did not interfere with the brightest stars aperture photometry). The only useful frames of M92 and Landolt stars (taken at low air masses and in photometric conditions) were from night 4 and the calibration curves - 6 1 -were assumed to be the same for every night. For these reasons we could not get an independent zero point for the C C D photometry and the magnitudes derived using OA's stars are the ones shown in all tables and light curves. Cudworth et al. 1986, found that the OA magnitudes were too faint in B and in V by 0 nl044. This correction has not been subtracted from the magnitudes presented in the tables. 3.2.3. The Results The results for the non-variable stars are summarized in Table V I . The stars' designations from this study and the OA numbers are given in the first two columns. B and V magnitudes were obtained by averaging the derived calibrated magnitudes from the 31 B and 7 V frames. Also listed are B - V colour indices, the number of measurements for each star and the standard deviation of the mean. A comparison between the results of OA and the magnitudes of this study is shown in F igs .18a and b . The plot VOA versus VOA — Vthia study in Fig . 18a presents an r.m.s. scatter about the zero line of 0™02 at 19™0 and 0™05 at 20m.0. Star 44 has a large deviation, as was expected, since it was often off the calibration curves. The positive trend at the faint end is due to the lack of faint calibration standard stars. This introduces uncertainties in the calculated magnitudes for the faint program stars, but this should not be a problem for the variable stars (their magnitudes range from 19™0 to 20^1 in V ) . The V magnitudes derived in this study are in agreement with the OA magnitudes for V brighter than 20n15. The plot BOA versus BOA — Bthis study hi Fig. 18b shows an r.m.s. scatter about - 6 2 -T A B L E VI PHOTOMETRY FOR T H E NON-VARIABLE STARS No. OA B n 0 \ B V n cry B-V &B—V 1 - 19.04 7 0.01 — — — _ _ 2 - 18.44 10 0.01 - — — _ 3 - 21.39 6 0.11 - — — _ 4 - 20.84 7 0.10 - - — _ _ 5 - 20.22 17 0.02 - - — — _ 6 - 20.37 8 0.11 - - — — — 8" 38 20.48° 28 0.02 19.79 6 0.01 0.69: 0.02 9" 284 21.28 9 0.09 20.78 5 0.02 0.50 0.09 10 295 21.35 12 0.05 21.26 1 — 0.09: — 11" 353 20.19° 21 0.02 19.97 6 0.02 0.22: 0.02 12 - 15.28 9 0.16 - - — _ _ 13 - 19.65 8 0.01 - - — _ _ 14 - 21.35 16 0.07 20.91 4 0.14 0.44 0.16 15 47 - - - 21.93 1 - — -16 - - - - 20.69 2 0.69 - — 17 - 20.95 19 0.02 20.40 5 0.04 0.55 0.05 18 - 18.44 24 0.00 17.56 6 0.02 0.88 0.02 19" 171 21.30 7 0.04 21.21 2 0.05 0.09: 0.07 20 b - 20.08c 18 0.01 19.82c 7 0.02 0.26: 0.03 21 - 20.14c 25 0.01 19.86c 7 0.03 0.28: 0.03 22 - 20.95c 4 0.09 20.54c 6 0.08 0.41: 0.12 236'" 57 20.16 27 0.01 19.41 7 0.02 0.75 0.02 24 - 21.15c 2 0.14 - - — — — 256-" 290 19.88 21 0.01 19.15 7 0.01 0.73 0.01 26 - 20.10 26 0.01 19.42 7 0.03 0.68 0.03 27 - 21.13 16 0.05 20.50 6 0.07 0.63 0.08 2 8 M 517 19.51 5 0.01 18.84 5 0.01 0.67 0.01 3 0 M 508 20.11 5 0.01 19.53 5 0.02 0.58 0.02 31 465 21.50 2 0.04 - - — — — 326'" 5 18.32 30 0.00 16.88 7 0.00 1.44 0.00 33 b - 19.79 28 0.01 19.04 7 0.01 0.75 0.01 34 - 19.76 21 0.01 19.09 2 0.01 0.67 0.02 35 - 20.81 2 0.11 - — — _ — 366'" 66 19.71 26 0.00 18.88 7 0.01 0.83 0.01 3 7 6 , « 139 20.75 21 0.01 20.05 7 0.02 0.70 0.03 386'" 113 19.45 21 0.00 18.57 7 0.01 0.88 0.01 39 62 20.06° 26 0.01 19.80 7 0.02 0.26: 0.02 40 76 21.87 1 - - - — — — 42 - 21.34 8 0.04 20.80 4 0.04 0.54 0.06 43M 300 19.92 14 0.01 19.12 7 0.02 0.80 0.02 44" 465 21.13 4 0.05 19.96° 7 0.02 1.17: 0.05 4 5 6 , « 260 21.14 18 0.07 19.75 7 0.01 1.33: 0.05 46 415 - - - 21.31 2 0.08 — -47 325 - - - 20.98 2 0.25 - — 486'" 209 20.21 26 0.01 19.49 7 0.02 0.72 0.02 TABLE VI (continued) PHOTOMETRY FOR THE NON-VARIABLE STARS No. OA B n V n B-V <rB_v 4 9 M 160 18.29 31 0.00 17.01 7 0.00 1.28 0.00 50 - 20.78 17 0.03 20.22 1 - 0.56 -51 288 22.02 1 - 21.31 1 - 0.71 -52 211 21.56 5 0.13 20.34 4 0.06 1.22 0.14 53 - 20.93 24 0.03 20.37 6 0.02 0.56 0.04 54 - 20.13 23 0.02 19.99 7 0.03 0.14 0.03 556 - 20.31 23 0.01 20.16 6 0.03 0.15 0.03 56 - 21.16 14 0.04 20.68 2 0.33 0.48 0.34 5 7 M 539 21.48 1 - 20.54 1 - 0.94 -5 8 M 544 20.91 2 0.06 20.23 1 - 0.68 -5 9 M 549 20.85 3 0.05 20.40 1 - 0.45: 60 - 20.81 19 0.03 19.61 6 0.04 1.20: 0.05 61 - 18.77 10 0.01 - - - - -62 - 20.95 6 0.02 19.97 6 0.03 0.98: 0.04 63 - 21.82 1 - 21.43 1 - 0.39: 64 - 21.03 16 0.03 20.56 1 - 0.47 -65 - - - - 21.41 1 - - -66 - 20.14 27 0.01 20.00 7 0.05 0.14 0.05 676,0 390 20.89 19 0.04 20.28 6 0.04 0.61 0.05 68 - 20.29 8 0.02 19.61 6 0.02 0.68 0.03 69 - 20.57 30 0.03 19.99 7 0.05 0.58 0.06 70 - 19.80 5 0.02 19.03 4 0.02 0.77 0.03 71 - 20.08 24 0.02 - - - - -72 - 16.84 8 0.10 - - - - -73 - 20.86 3 0.09 - - - -74 - - - - 21.07 2 0.13 - -75 - 20.22 5 0.01 . 19.53 5 0.04 0.69 0.04 76 - 22.02 1 - 21.31 2 0.32 0.71 : -77b - 20.11 18 0.01 19.98 6 0.06 0.13 0.05 786 - 18.78 21 0.01 17.72 7 0.01 1.06 0.01 79 - 20.18 18 0.02 20.03 6 0.04 0.15 0.04 80 - - - - 21.25 1 - - -81 - 20.75 15 0.04 20.14 7 0.05 0.61 0.07 82 - 20.71 3 0.01 20.06 1 - 0.65 -83 - 21.69 2 0.04 - - - - -84 - 17.44 1 - - - - - -85 - 20.86 1 - - - - - -86 745 18.92 1 - - - - - -87 660 20.14 1 - - - - - -88 731 21.13 1 - - - - - -89 - 20.17 1 - - - - - -90 612 18.90 1 - - - - - -91 710 20.33 1 - - - - - -92 698 21.88 1 - - - - - -93 663 20.29 1 - - - — — — " V calibration star; 0 Magnitude is fainter by ~ 0.1 mag than that published by OA; 6 B calibration star; c Photometric magnitude contaminated by nearby star. - 64 -.6 .4 .2 AV 0 - . 2 -.4 - . 6 .6 .4 .2 i ) V ( O A ) - V ( K P 3 6 C C D ) w -I I l_ J I l_ _l I l_ 17 18 1 9 V ( 0 A ) 2 0 . 21 22 AB 0 -.2 — -.4 — -.6 — | — r — i — i — | — i — i — i — | — i — i b ) B ( O A ) - B ( K P 3 6 C C D ) ~i—i—r j ' ' 17 18 B ( O A ) 21 22 .8 .6 .4 AB -2 0 - . 2 --.4 \ -- . 6 c ) B ( v a n A g t ) - B ( t h i s p a p e r ) • P60 pt o KP36 CCD 19.4 19.6 19.8 20.0 B(P60 p g ) 20.2 20.4 Fig. 18 — Comparison between the OA magnitudes and the (a) V and (b) B magnitudes derived in this study. The scatter at the faint end is due to the larger errors associated with the photometry of faint stars and to the lack of faint calibration stars. In (a) the point in parentheses is star 44, which was systematically fainter than the value published by OA. In (b) the stars in parentheses are stars 86 and 87, which were measured in only one KP36 CCD frame and stars 11 and 39, which were systematically fainter than the magnitudes given by OA. These stars were not used as standard stars in the reductions. There is good agreement between the magnitudes derived in this study and the magnitudes from OA, for stars brighter than 20™6 in B and 20™5 in V. c) — Comparison of mean magnitudes for KP36 CCD, P200 pg and P60 pg data. There is a systematic difference between the old and the new data. This is probably due to systematic errors in the photographic transfers, which were done to calibrate the P200 pg data. The difference between the P60 pg and the KP36 CCD photometry amounts ~ 0^1. The possible causes for this discrepancy are discussed in the text. -65 -the zero line of 0™05 at 20^5, and 0^2 at 21™0. Stars 11 and 39 have a large deviation, as was expected since they were often off the calibration curves. The magnitudes of stars 86 and 87 from this study differ by about O ^ l from the OA magnitudes, but since these stars were measured in only one KP36 C C D frame, the true magnitude cannot be stated. There is good agreement between the results obtained by OA and the results of this chapter for stars brighter than B=20™60 (safe results for the variables that range from 19m.l to 20™5 in B) . The scatter seen at magnitudes fainter than 21m.O is due to the larger errors in the photometry of the faint stars and to the lack of faint calibration stars. The magnitudes for the seven variables are given in Tables V I I and V I I I . Table I X summarizes the variable types, periods and the minimum, maximum and mean magnitudes. The mean B magnitudes listed in column 4 were derived through the transformation of magnitudes into flux, averaging over the entire light curve and trans-forming back to magnitudes. The mean V magnitudes in column 7 were derived in the same way, with exception of stars V58, V59 and V97, for which the measurements are spread over a small phase coverage. A n eye-estimate of the mean was done in these cases. The average mean B and V magnitudes for the five c-type R R Lyraes stars are < B > = 20™14±0 n?06(s.d.m.) and < V > = 19™90±0™05 (s.d.m.). 3.3. A N A L Y S I S OF T H E C O M B I N E D P H O T O G R A P H I C A N D C C D D A T A Three sets of photometry were available for the seven variable stars: the photo-graphic plates taken by W.Baade with the Palomar 200 inch (5 m) telescope and - 6 6 -T A B L E VII B MAGNITUDES FOR T H E VARIABLES Hel.J.D. 2445000+ V97 V95 V83 V59 V58 V57 V55 852.7944 20.19 20.18 20.20 19.99 20.21 — 20.08 852.8354 20.26 20.25 20.39 20.14 19.87 - 20.31 852.8750 20.27 20.09 - 20.07 19.86 - 20.23 853.7548 20.32 20.18 20.31 19.45 20.26 20.05 -853.8055 20.43 - - - - 20.27 20.58 853.8249 20.40 - - 19.32 20.40 20.18 20.49 853.8450 - - - 19.45 20.33 20.19 20.54 853.8860 20.38 - 19.94 19.70 19.85 20.16 20.56 853.9221 20.43 20.17 19.95 19.88 - 20.29 19.65 854.7478 20.43 19.94 20.08 20.11 20.30 854.7673 - - 19.93 20.03 - 20.31 20.13 854.7895 - 20.05 20.18 19.96 20.38 - 20.08 854.8103 - 20.01 20.14 20.16 20.35 20.07 20.11 854.8325 20.12 - - 20.01 20.35 20.09 20.40 854.8548 20.21 20.15 20.25 20.19 - - 20.44 854.8728 - 20.06 20.37 19.96 - - -854.8874 19.98 - 20.40 19.94 20.25 - -854.9062 20.27 20.08 20.29 19.69 - 19.93 20.30 854.9284 20.03 20.16 20.42 19.45 19.89 - 20.28 854.9464 20.13 20.02 20.46 19.25 19.91 - 20.45 854.9610 20.09 20.30 20.38 19.22 19.81 20.25 20.39 855.6735 - 20.01 20.34 19.95 - -855.7055 20.07 20.02 20.32 19.53 19.85 - 20.48 855.7291 20.13 - - 19.25 19.85 20.00 20.55 855.7562 20.17 - - 19.15 - 20.08 20.56 855.7770 20.14 20.06 20.27 19.30 20.08 20.10 20.41 855.8645 20.08 20.24 19.93 - 20.37 20.24 20.59 855.8860 20.29 20.23 19.99 19.91 20.40 20.34 20.36 855.9138 20.18 20.17 19.85 19.90 20.34 - 19.64 855.9346 20.28 20.09 19.94 20.04 20.20 20.24 19.43 855.9555 20.17 20.05 19.98 19.95 20.20 20.29 19.46 - 67 -T A B L E VIII V MAGNITUDES FOR T H E VARIABLE STARS HJD 2445000+ V97 V95 V83 V59 V58 V57 V55 852.8194 19.68 20.01 19.94 19.70 19.73 19.93 19.88 852.8542 19.92 20.00 20.13 19.67 19.68 20.03 20.09 852.8944 19.86 19.96 20.14 19.73 19.65 20.05 19.98 852.9174 19.85 19.77 20.03 19.75 19.71 20.03 20.09 853.8624 19.85 - - 19.19 19.89 19.97 20.19 853.8999 20.01 19.80 19.59 19.38 19.59 19.94 19.85 853.9423 19.89 19.86 19.55 19.69 19.55 19.88 19.17 -68 -TABLE LX PHOTOMETRIC PROPERTIES OF THE SEVEN VARIABLES Star Type Period <B> Bfnax <V > v ¥ max (1) (2) (3) (4) (5) (6) (7) (8) (9) V55 ab 0.663579 20.08 20.52,. 19.43 19.75 20.40 19.33 V57 c 0.404924 20.15 20.30 20.03 19.98 20.05 19.85 V58 c 0.351432 20.07 20.40 19.82 19.90 20.2: 19.42 V59 aC 0.389981 19.71 20.17 19.15 19.49 20.00 18.98 V83 c 0.406575 20.13 20.40 19.91 19.83: 20.14 19.57 V95 c 0.439352 20.10 20.23 20.00 19.92 20.00 19.78 V97 c 0.430093 20.24 20.40 20.11 19.89: - -- 69 -photometrically measured by van Agt (hereafter called P200 pg data); a series of 22 photographic plates taken by Drs. J . M . Nemec and R . M . Rich with the Palomar 60-inch (1.5 m) telescope in July and August 1984, and measured by Dr. A . F . Wehlau (hereafter P60 pg); and the KP36 C C D frames described in the present study (photometry given in Tables VII and VIII). By combining all these data, accurate periods and colours are derived for the seven variables. A comparison of these three sets of data (KP36 C C D , P60 pg and P200 pg) for all the variables in the Ursa Minor dwarf galaxy is shown in Fig .18c. The solid and open dots represent, respectively, the difference between the P200 pg data and the two sets of new photometry (P60 pg and KP36 C C D ) . A large zero point difference is seen between van Agt's photometry and the new photometry, which is probably due to systematic errors introduced in the photographic transfers made to calibrate the P200 pg data. What was not expected is the lack of agreement between the P60 pg and the KP36 C C D mean magnitudes. For the seven stars in common, these systematic differences are shown by short lines joining the two results. The B C C D magnitudes for these variables are systematically ~ 0™1 fainter than the photographic results. This discrepancy could be a result of the slightly different sets of O A standard stars used for calibration of the photometry. It could also be a result of different effective transmission bands of the filters used in obtaining the C C D and photographic data. About 23 standards were used to calibrate the photographic B plates (NWO). From these, seven were not used to calibrate the B C C D frames from nights 1 and 2 because they were either too faint, systematically off the calibration curves, or off the C C D frames. For nights 3 and 4 (the majority of the frames), only eight standards were in common with the ones used to calibrate the photographic plates. However, this discrepancy in the mean magnitude level for the variable stars did not affect the period searches, except for the star V95 which is a very low amplitude R R Lyrae star. For this variable the P200 pg and P60 pg data were shifted to a common mean magnitude, set by the KP36 C C D data, in order not to introduce spurious periods into the analysis. 3.3.1. Period Searches Pulsation periods for the variables were determined using phase dispersion min-imization (PDM) techniques (Lafier and Kinman 1965, Stellingwerf 1978 and Nemec 1985a,b). The Stellingwerf's 0 transform 0(P) is a measurement of the dispersion of the observations about the mean light curve for each trial period P. When 6 is minimized, the most probable period is obtained. F ig .19 shows 0 transforms for period searches done in six different period intervals for V58. This is a sample of the procedure fol-lowed for each variable. In every case, a coarse period search (over a large range of periods) was performed to check the period suggested by Kholopov (1971) and the two closest alias determined by the imposed one-day period in the observations. Period searches in other period intervals were also done, but in all cases the period estimated by Kholopov, or one of the alias periods ((1/P) ± 1 = (l/PaUas)) turned out to be the correct one. Finer period searches were then done, over a small range of periods and in steps of 0^000001 or less, allowing more accurate periods to be derived. Various VAR 58 w i i i I i i i I i i i | i i i | i "I P=0?259854 ' • • • i .256 .258 260 262 .264 T i | i i i i - 1 i - n r - r h P=0?259853 i i I i i i .2600 PERIOD 1.2 l I I I I l I l I I I l I l I I I I - P=0?351433 i i i o.* .346 .346 .350 .352 .354 .356 1.2 I I I I I I I I I I l l I I I I I I P=0:351432 I !• I I I I" I I 1 I I I I I I I • • I .3505 .3510 .3515 .3520 PERIOD 0.4 -i—|—i—i—i—|—i—r—i—|—i—i—r P=0?542663 .544 £46 I I I I I I I I I I I I I I I I I I P=0T542662 • • • < ' i i i i i i i t £420 £425 .5430 .5435 PERIOD Fig. 19 — For V58, coarse period searches, using all the available data (P200 pg, P60 pg and KP36 C C D B) , in steps of 0^000007 (a) — from 0^255 to 0^265; (b) — from 0^346 to 0^356; (c) — from 0^539 to 0^546. Finer period searches, using the same data, in steps of 0^000002 (d) — from 0^2597 to 0^2610; (e) — from 0^3504 to 0^3524 and (f) from 0^5416 to 0^5436. The most probable periods in each interval are shown above the panels and the corresponding minimum <?'s are 0.49, 0.47, 0.51, 0.51, 0.42 and 0.49 respectively. The theta transforms and the light curves suggest that the period for V58 is 0^351432. The real time plot of the KP36 C C D B data confirms this period. - 72 -aspects were considered in order to decide among the true and the alias periods: the real time light curves, the symmetry of the 0 transforms, the minimum 0's, the shape of the light curves, and the star's positions in the period-amplitude diagram (NWO). The real time plots were not useful in many cases as there were only a few observations per night. Light curves for the two most probable periods were plotted whenever the correct period was not obvious from the 0 transforms. 3.3.2. Notes on the Seven Variable Stars V55 -The 0 transforms for three different intervals are shown in Fig.20. The period is 0<?663579 and light curves for all the data, using this period, are plotted in Fig.21. No period change seems to have occurred in the last 30 years, as can be seen by comparing the phases of maximum light for the older and more recent data. V57 - Van Agt (1967) suggested a period of 0^40 for this star, and Kholopov (1971) suggested 0^287986. A period search using all the data (Fig.22) suggested that the most probable periods are 0^287991 (6min=0.56) and 0^404924 (0 m i n =O.63). It was difficult to decide between these two periods from the 6 transforms and the light curves alone since the minimum 0's were very similar and the light curves show considerable scatter. Both periods look equally plausible when light curves using all the available data are plotted (see Fig.23). The shorter period would put V57 in a peculiar position in the period-amplitude diagram (NWO), to the left of the c-type distribution. The plot in real time of the KP36 C C D B data, despite the scatter, seems to rule out the shorter period. With a period of 0^404924, V57 is at the tail of the c-type distribution Fig. 20 — For V55, 6 transforms for period searches, using all the data, in steps of 0^000001. The minimum 0's corresponding to the most probable periods in these three intervals are 0.34, 0.51 and 0.63 (from longer to shorter periods). The correct period is 0^663582 (which is confirmed by the real time plot of the KP36 C C D B data). V55, P=0.663582 19.0 B 20.0 21.0 19.0 - 1 1 1 : K P 3 6 1 1 CCD *x 1 1 ; r X : - x*xx : *x y : , I , X * 1 1 & ~ X XX-*x # . 1 -0 1 19.0 — i 1 1 1 1 r - K P 3 6 CCD V 20.0 * * * -B 20.0 i i i r : . P60 pg 19.0 B gc© P 2 0 0 pg - 20.0 21.0 1 L. ' ' l l_ 21.0 n r i rammn _ J O O Dp O G&o <STO O O OOdEOO I ' I I 1_ , o X PHASE 0 1 P H A S E Fig. 21 — Light curves for V55 plotted with the period of 0a663582 and using all the data available: KP36 CCD B data (crosses), KP36 CCD V data (asterisks), P60 pg data (solid dots) and P200 pg data (open circles). - 75 -VAR 57 F i g . 22 — For V 5 7 , 0 transforms for period searches using a l l the data, in steps of 0^0000001. The m i n i m u m 0's corresponding to the periods indicated above each panel are 0.78, 0.63 and 0.56 (from longer to shorter periods). Since the values of m i n i m u m 6 are very similar , it should not be the only criterion used to decide which is the best period. The most probable period is P=0'?404924, for the reasons described i n the text. - 76 -VAR 57 P=0.287991 P=0.404924 19.5 20.0 20.5 20.0 19.5 20.0 20.5 1 1 1 1 1 1 l . . 1 1 ' 1 ' 1 1 . 7 KP36 CCD — 19.5 7 KP36 CCD -- - B -X 20.0 X x x x\ Ji xx x * x x * ; * % x : x x xS x x -* * X v X > x*x x - * x x *x -1 1 1 1 1 , 1 " 20.5 • , i , . . . i • 0 1 0 1 _ 1 1 1 1 1 -_ KP36 CCD ' 1 . 19.5 _ 1 1 1 1 . . , _ •_ KP36 CCD j L • « * •* .. •« V 20.0 "«•* * • • * • " » *• ~« 1 1 1 1 1 I 1 ~ 20.5 ^ , l , , , , 1 0 1 0 1 _ 1 1 1 1 1 7 P60 pg 1 1 . 19.5 B . ' 1 1 1 1 1 1 . 7 P60 pg -L . •*> • 20.0 • *•* • • * . j • • :• * ' • * - 20.5 - -i I i i i 1 1 " i i i i t i i 19.5 B 20.0 20.5 - i — | — i — i — i i — r P200 pg o o 20.0 - i 1 1 r P200 pg PHASE Fig. 23 — Light curves for V57 plotted with the most probable periods. The shorter period is an alias. Symbols have the same meaning as before. The phase of maximum light in V shows a large and unusual shift with respect to the phase of maximum light in B. This shift cannot be explained by observational errors. in the period-amplitude diagram. As can be seen in Fig. 23, the phase of maximum light in V shows a large and unusual shift with respect to the phase of maximum light in B . This shift cannot be explained by observational errors. V58 - Coarse and fine period searches were done for this star, and the 0 transforms are shown in Fig . 19. Period searching all the data, the two most probable periods were found to be P=0<*259853 (0 m t n =O.5l ) and P=0<*351432 (0 m t n =O.42). The light curves plotted with these two periods using all the data available (Fig.24) suggests that P=0C?351432 is the correct period. V59 - The 0 transforms in Fig .25 suggest that P=0£?389981 is the correct period for this star. Light curves using this period and all the data available are shown in Fig .26 . The period and amplitude of V59 are in the same range as for R R Lyrae stars, but <B> is ~ 0^4 brighter than the average <B>for the other 6 R R Lyraes. It is therefore considered an anomalous Cepheid. A discussion of anomalous Cepheids in general, and V59 in particular, is contained in § 3.4.4. V83 - The 0 transforms for three different intervals are shown in Fig .27. In Fig .28 light curves using all the data plotted with the two most probable periods P=0^686420 and P=0£?406575 are shown. Both these periods fit on the period-amplitude diagram (NWO) equally well, one placing the star in the c-type distribution, the other among" the ab's. The shape of the light curve and the real time plot suggest P=0C?406575 is the correct period. V95 - In Fig . 18c it was shown that the P200 pg photometry, the P60 pg VAR 58 P=0.259853 P=0.351432 19.5 20.0 -20.5 i 1 1 1 1 r~ KP36 CCD I ' l l ' 19.5 B 19.0 19.5 20.0 20.5 i 1 1 1 1 r KP36 CCD _i i i i_ 20.0 20.5 19.0 19.5 20.0 -20.5 -. ' 1 1 1 1 ' 1 . 7 KP36 CCD 1 : ^ " x x x --xx - x V x V - x M X X x X " , 1 , , xx ** x * , , 1 -0 1 KP36 CCD _1 I I L_ 19.5 20.0 -I [• 1 1 1 1 • P60 pg • • • •< _l 1 I L. B 20.0 - i — F — i — . — i — . — p — 7 P60 pg« • • • -• • • ' * • _ . i . . i : B -o 20.5 P200 pg OD 0 0 '<§b 2. b O Q 0 D o o C <K8,8P °O\ M o _i i i i_ PHASE 19.5 Fig. 24 — Light curves for V58 plotted with the most probable periods. The shorter period is an alias. Symbols have the same meaning as before. - 79 -VAR 59 1.2 0.4 0.2 II I I I I I I I I I I I I I | M I I I P=0:280351 JLl ' I I ' ' I ' ' I 1 ' ' I I ' I I I 1.2 I I I I I I I I I I I I I I I I I I I P=0?389981 .2798.2800.2802.2804.2806.2808 PERIOD 0.6 -0.4 -0 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 .3890 .3895 .3900 .3905 .3910 PERIOD .6385 .6390 .6395 .6400 PERIOD Fig. 25 — For V59, 0 transforms for period searches using all the data, in steps of 0^000002. The minimum 0's corresponding to the periods indicated above each panel are 0.39, 0.28 and 0.58 (from shorter to longer periods). The most probable period is 0^389981 (which is confirmed by the real time plot of the KP36 C C D B data). - 80 -V59, P=0.389981 19.0 B 1 1 1 1 r K P 3 6 CCD X * 20.0 * * * * x< * * x x x I I L Xx X x„ _l 1_ 18.0 V 19.0 20.0 T ~i 1 r r K P 3 6 CCD * » * »* J i i _ ~i 1 1 r 19.0 P60 pg B i- • 20.0 • • • J I l_ 19.0 P L B 20.0 - i 1 1 1 1 r o P 2 0 0 pg , o o t- ° CO o dPcPo' J I I 1_ jbj) O O o CO CL 0 1 P H A S E 1 P H A S E Fig . 26 — Light curves for V59 plotted with the most probable period. Symbols have the same meaning as before. - 81 -VAR 83 Fig. 27 — For V83, 6 transforms for period searches using all the data, in steps of 0^000001. The minimum 0's corresponding to the periods indicated above each panel are 0.84, 0.45 and 0.53 (from shorter to longer periods). The most probable period is 0^406575. - 82 -VAR 83 P=0.406575 P=0.686420 19.5 20.0 20.5 -i 1 1 1 1 r KP36 CCD X _l I L. 19.0 19.5 — 20.0 --i 1 1 1 1 r KP36 CCD i I I - i 1 1 r - P60 pg 20.5 _i I i_ 20.0 20.5 - 19.5 20.0 20.5 1 1 1 1 1 - KP36 CCD 1 1 . X : x -_ V 1 1 1 1 1 , 1 " 0 l 1 | 1 1 1 : KP36 CCD 1 1 . r •* — • ** i i i i i * • — »* " , 1 " 0 l 1 j 1 1 1 - P60 pg 1 A • • • • 1 1 . • — • • — • i ! i i i • — 19.5 20.5 - i 1 1 1 1 r P200 pg - B -°Pr->? O ° fc ooo 8 -OfWP" o_ ' O f t p o °°< • ° oxftaPo ° e oo C S D O O al i I i i i i I 0 1 PHASE 19.5 20.0 P200 pg 6% c9. . OD o 9 o i(j> O O P ^ a> po oc 0 1 PHASE F i g . 28 — Light curves for V 8 3 plotted wi th the most probable periods. The longer period is an alias. Symbols have the same meaning as before. - 83 -photometry and the KP36 C C D photometry were systematically different, with the P200 pg data being the faintest. Since these differences could influence the result of a period search (this star has very low amplitude), the P60 pg data was shifted faintward by 0^08, and the P200 pg was shifted brightward by 0m.l (i.e. a -0m.l shift), in order to get a common mean set by the KP36 C C D data. Some discordant data from P200 pg were rejected. Period searches were then done in three different intervals. F ig .29 shows the 6 transforms with the three most probable periods indicated: 0^233607, 0^305067 and 0^439352. The minimum 0 values are 0.58, 0.54 and 0.58 respectively. The light curves plotted using the two longer periods with all the data, are shown in F ig .30 (P60 pg and P200 pg are shifted in this plot). It is very difficult to decide which is the correct period from the 0 transforms and light curves alone. The shortest period, P=0*234 seems improbable because it places the star in a singular position in the period-amplitude diagram (NWO), far to the left of the c-type distribution. In F ig .31 the KP36 C C D B data are plotted in real time. Measurements for only two nights are used in this plot (2/3 and 3/4 of June 1984) since no more than three measurements are available for the other nights. According to the real time plot, the longer period, P=0£?439352, seems to be the most appropriate for this variable. V97 - The P200 pg data for this star was given in an arbitrary scale (in steps from 0 to 68). Period searches were done using all the available data with van Agt's arbitrary scale shifted to the level of the KP36 C C D data (step 0 matched with magnitude 19^80 and step 68 with 20™48). The most probable periods suggested by the searches were 0^430093 and 0^756259 (Fig.32). Van Agt did not determine a period for this star; - 84 -VAR 95 Fig. 29 — For V95, 0 transforms for period searches, in steps of 0^000001, using all the data shifted to a common mean magnitude set by the KP36 C C D B data. The minimum 0's corresponding to the periods indicated above each panel are 0.58, 0.54 and 0.58 (from shorter to longer periods). The most probable period is P=0<?439352 for the reasons described in the text. - 85 -VAR 95 P=0.305067 P=0.439352 B 1 KP36 CCD ' 1 1 B 1 , 1 1 1 , , - KP36 CCD 20.0 X x x >• X * x x ~ *: X 20.0 X X — x x x x X X XX x x _ XX X XX x x # x * x * * X X x v X s* x_ X X X X X -x x x x x x x x x X vX X * X X 20.4 1 , , , - 1 20.4 , 1 1 1 1 1 I 0 1 0 1 19.5 1 1 1 1 KP36 CCD ' ' 1 19.5 1 , 1 1 1 1 , 7 KP36 CCD ~ V * * * • • V * • * »-• 20.0 1 • • • i < , , , 1 20.0 • • . 1 0 1 0 1 B 20.0 1 • 1 1 1 P60 p g • V 1 1 B 20.0 1 , 1 1 1 1 , - P60 p g • • • • . .... . -.-20.4 1 , , < 1 20.4 1 1 1 1 1 1 1 0 1 0 1 B 1 1 1 ' P200 p g 1 B 1 , 1 1 1 1 , - P200 p g 20.0 0»0_Q 20.0 0 0 D0°O ~ °J o oogJoo^B | ° o 8d38 oo°o o "c oS°° o " °8 £ <b 20.4 t 1 . . , 1 20.4 • 1 1 1 1 1 1 0 0 1 PHASE PHASE Fig. 30 — Light curves for V95 plotted with the most probable periods. The shorter period is probably an alias. The P60 pg and P200 pg data are shifted by 0™08 and - 0 " l l , respectively, as explained in the text. Symbols are the same as before. - 86 -VAR 95 19.8 i l l i | i i i NIGHT 3 • l | l l i l | i i NIGHT 4 i i 20.1 — • • • • • • • • • • • • — 20.4 i i i 1 i i i i 1 i i i i 1 i i 45854.5 45855.0 45855.5 45856.0 45856.5 JULIAN DATE (2400000+) Fig. 31 — For V95, the KP36 C C D B data is plotted in real time for the nights 2/3 and 3/4 of June 1984. Despite the scatter present, it seems that P=0^305 can be ruled out, with the longer period, P=0^439352, being the correct one. This plot exemplifies the difficulty involved in ruling out aliasing periods when only a few observations per night are available. - 8 7 -VAR 97 1.2 H W E-1 0.8 0.6 0.4 | I I I I | I I I I | P=0?349084 1.2 T—I—i—i—i—I—i—i—i—I—r I 111 I P=0?430093 0.6 0.4 0 2 1 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 0.2 I 1 I 1 1 ' I 1 1 1 I 1 .346 .347 .348 .349 .350 .351 .4280 .4300 .4320 1.2 T - | i i i i | i r~ P=0?756259 PERIOD PERIOD 0.6 0.4 0.2 .750 .755 .760 PERIOD Fig. 32 — For V97, 6 transforms for period searches, in steps of 0^000001, using all the data as described in the text. The minimum 0's corresponding to the periods indicated above each panel are 0.60, 0.40 and 0.41 (from shorter to longer periods). The light curves plotted in Fig. 33 suggest that P=0^430093 is the correct period for this star. - 88 -Kholopov found P=0^430083. The light curves using both possible periods and all the available data are shown in Fig .33 and they suggest that P=0£?430093 is the correct period for this star. 3.4. DISCUSSION 3.4.1. Colour-Magnitude Diagram For the first time, very accurate mean colours for R R Lyrae stars in the Ursa Minor dwarf galaxy are derived. In Fig .34 the C M D is plotted and the horizontal branch stars given by OA are included in order to better define the limits of the instability strip. Also plotted are the non-variable stars with accurate photometry from this study (see Table V I , stars with colons are not plotted). There were three stars in the instability strip in OA's C M D : stars 63, 85 and 1269. Stars 63 and 85 correspond to V55 and V57 respectively and star 1269 is a blue horizontal branch star (NWO). The limits of the instability strip are at (B-V) ~ 0™16 ±0m.02 and 0 n ^40±0 n i05, considering the seven variables from the present study and the horizontal branch stars plotted in Fig. 34. The blue edge of the instability strip has been determined quite accurately since three of the R R Lyraes in this study are very blue c-types and there are ten blue horizontal branch stars from O A and another five from this study. The red edge of the gap is set with greater uncertainty than the blue edge, since there is only one ab-type R R Lyrae star with known colour and only two red horizontal branch stars measured by OA. - 89 -VAR 97 P=0.430093 P=0.756290 -i \ 1 1 1 r KP36 CCD B — 20.0 — * x x X X v X * x x x x x _l I I L. 20.5 i 1 1 1 1 r KP36 CCD . xx -X*x x * * x x * X x* *x x x* *x JL 19.5 20.0 - 1 — I — I — . — I — I — r KP36 CCD 19.5 n 1 1 1 1 r KP36 CCD # * # * • -• — _i i i i i i— B 20.0 20.5 -i 1 1 r P60 pg •••• • _1 I L. B 20.0 20.5 -— i — i — i — i — i — i — r P60 pg _l I I !_ B 20.5 P20Q B g <^ 3> O O O I X I D co - B JI ooc o ooa» oaooaamo ooa» _L _i i i i_ - i 1 1 1 1 r P200 p & 0 o9 C # > Q5> DOO OCX) O O O d H S O o c 8 _l I I [_ 0 1 PHASE 0 1 PHASE Fig . 33 — Light curves for V97 plotted with the most probable periods. The P200 pg, data originally given in arbitrary units, is shifted as described in the text. The longer period is an alias. Symbols have the same meaning as before. - 9 0 -16 V 18 20 l I I I I I I i i I I l l I I I l I I I I I I i i I i i i I i i i I i i i | i I URSA MINOR 11111 * 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -2 0 .2 .4 .6 .8 1 1.2 1.4 1.6 B - V Fig . 34 — Colour-magnitude diagram for the stars in the Ursa Minor dwarf galaxy showing the position of the seven variables described in the text. The large filled and open circles indicate the ab and c type R R Lyrae stars, respectively. The triangle is the anomalous Cepheid V59. The small filled circles are non-variable stars with accurate photometry determined in this study (Table VI) . Also plotted are horizontal branch stars observed by O A (crosses). The lines at (B-V) = 0™16 and 0™40 are best estimates of the limits of the instability strip. - 91 -3.4.2. The c-Type RR Lyrae Stars in Ursa Minor The five c-type R R Lyrae stars described in this study have colours ranging from 0m.17 to 0™35. The very red colour of the longest period c-type R R Lyrae star deter-mined in this study suggests that there is an overlap in the B - V colors of the ab and c-type R R Lyrae stars. A n overlap in colours of the RRab's and RRc's is seen in the Galactic globular clusters M15 and u Cen but it is not observed in the Oosterhoff type I globular cluster M 3 . The accurate magnitudes and colours for the RRc's derived in this study allow a new distance determination for the Ursa Minor spheroidal galaxy to be made. In distance determinations the level of the horizontal branch (HB) is usually adopted as the magnitude of the blue edge of the R R Lyrae gap (Webbink 1985). The mean magnitudes of the three c-type R R Lyrae stars at the blue edge of the instability strip V57, V58 and V95 were averaged giving a value of <V>=19™93±0™04 for the H B level. After making <V> brighter by 0"1044 to account for the "note added in proof" in the O A paper, assuming E(B-V)=0.02±0.01 (Zinn, 1981), A y = 3 E ( B - V ) and My=0™6±0™2, a distance modulus of 19™23±0™27 was derived. This value is ~ 0^23 fainter than the distance modulus obtained by Cudworth et al. and OA. The major source of error is the large uncertainty in the value of M y . According to N W O , there are 35 c-type R R Lyrae stars in the Ursa Minor spheroidal galaxy (43% of the R R Lyrae stars), and they have a mean period of 0^375. Both the mean period and the relatively high fraction of c-type R R Lyrae stars are consistent with the Ursa Minor dwarf galaxy being an Oosterhoff type II system with a low mean - 9 2 -metallicity. 3.4.3. Search for Double-Mode RR Lyrae Stars in Ursa Minor Double-mode R R Lyrae stars (RRd's) are very important, in the sense that from their periods and approximately constant period ratios (first-overtone over fundamen-tal), masses can be calculated from pulsation models (Petersen 1973, and Cox et al. 1980) and absolute magnitudes and differential metal abundances can be derived. At present, three globular clusters: M15, M3 and IC4499 (Cox et al. 1983; Clement et al. 1986; Nemec and Clement 1988) and the Draco dwarf galaxy (Nemec 1985a) are known to possess RRd's . On the other hand, extensive searches in to Cen (Nemec et al. 1986) and in M5 (Nemec and Clement, unpublished) have found none. The range in periods and metal abundances of the known RRd's is important in guiding the search for new double-mode R R Lyrae stars in other systems. The globular cluster M15 ( [Fe/H] = -2.1 ) has 14 double-mode stars with primary periods in the range 0^39-0^43. Mean masses of 0.65 M© (Cox et al. 1980) were derived for these stars. The Draco dwarf spheroidal galaxy ([Fe/H] from -1.8 to -2.9) has 10 double-mode R R Lyraes, nine of which have primary periods in the same range as the double-mode R R Lyrae stars in M15, and one similar to the ones found in IC4499 and M 3 . These two clusters have intermediate metal abudances, and contain double-mode R R Lyrae stars with primary periods ranging from 0^35 to 0^37 and masses close to 0.55 M Q . Except possibly for V68 in M3 (Nemec and Clement 1988), the dominant mode of pulsation of RRd's is the first-overtone mode. Double-mode R R Lyrae stars are usually identified - 9 3 -among the longest period c-type R R Lyrae stars in a given system. From the information above, one would expect to find double-mode stars in the Ursa Minor dwarf galaxy, if they exist, among the c-type R R Lyrae stars with periods longer than 0^38 (since the Ursa Minor dwarf galaxy is known to have a low metal abundance). The analysis described here was done using all the available photometry on the variables in the Ursa Minor dwarf galaxy. From the 33 c-type R R Lyrae stars in Ursa Minor, only eight have periods in the range 0^38 to 0^43: V27, V44, V49, V57, V68, V73, V81 and V83. Seven stars have periods from 0^43 to 0^45: V9 , V12, V61, V79, V84, V95 and V97. As does u> Centauri, the Ursa Minor dwarf galaxy contains a few very long period c-type R R Lyrae stars. From the fifteen candidates, only V44, V49, V57, V83, V84, V95 and V97 could be checked for double periodicity. For all the others, only P60 pg data were available (measurements taken in eight nights spread over an eleven-day baseline) which was not extensive enough (very short baseline) to find a secondary component (if it exists). The search procedure was similar to that described by Nemec (1985a,b). F ig .35 shows the 0 transforms for the residuals, obtained by prewhitening the P200 pg, P60 pg and KP36 C C D data (when available) with the primary periods indicated above each panel (these periods are from Table VII of NWO) . No significant features are presented, no symmetric sidelobes are seen and the minimum 0 in every case is higher than 0.8. Comparing these 6 transforms with the ones of double-mode R R Lyraes found in the Draco dwarf galaxy (Nemec 1985a), it is concluded that V44, V49, V57, V83, V84, V95 and V97 are not double modes. - 9 4 -i I - 1 1 i |—i—i—i—|—i—i—i—|—i—i—i—|—r V 3 8 - P = 0 . 3 5 6 9 7 4 J — i — i i i i i i i i .46 .48 .52 V 4 4 - P = 0 . 3 8 1 9 8 0 _l I l I I u J I I I I I I ' I .48 .5 .52 .54 V 4 9 - P = 0 . 4 1 5 2 8 9 i i i i i i i i i i i i i i i i i i i i i i i i i i i .5 .52 .54 .56 .58 .6 V 5 7 - P = 0 . 4 0 4 9 2 4 ' ' ' I I 1 L I • • • I • . • I .52 .54 .56 .58 V 5 8 - P l = 0 . 3 5 1 4 3 2 I ' l l I I I 1 I l _ l 1 1 L. 42 .48 .48 PERIOD .52 ~l | 1 I I |—I—1—I—|—I—1—I—|—I—I—I—|—r V 5 9 - P = 0 . 3 8 9 9 8 1 J - U I I I I I I I ' I I I •48 .5 .52 .54 .56 V 8 3 - P = 0 . 4 0 6 5 7 5 •52 .54 .58 .58 V 8 4 - P = 0 . 4 3 2 7 1 8 -i—i—i i i I i i i i i i i i ' ' i i i _L I 1 1 i i -J 1 1 1 I I I I I I I .54 .56 .58 .6 .62 V 9 5 - P = 0 . 4 3 9 3 5 2 i i i i i L I I I I 1 L_ .56 .58 .62 V 9 7 - P l = 0 . 4 3 0 0 9 3 i i i i i i i i i i i i i I — i — i — i — i — i -.54 .56 .58 .6 PERIOD .62 Fig. 35 — 0 transforms for V38, V44, V49, V57, V58, V59, V83, V84, V95 and V97. Period searches were done using residuals, after prewhitening all the data with the main periods (indicated above each panel). The main periods are from Table VII of N W O . The minimum 6 is in every case higher than 0.8. The expected secondary periods (from the expected ratio for double mode R R Lyrae stars Pl /P0~0.74) are approximately in the middle point of each scale. No significant features are seen which suggests that none of these stars are double mode R R Lyrae stars. - 9 5 -V59 (P=0<*390) was also investigated, since its period is near that of the R R d stars in M15, despite the fact it is believed to be an anomalous Cepheid. No evidence for a secondary oscillation was seen. If the Ursa Minor dwarf galaxy has a spread in metal abundance similar to that of the Draco dwarf galaxy (Stetson 1984 gives [Fe/H] for the Ursa Minor dwarf galaxy ranging from -1.8 to -2.2 and for the Draco dwarf galaxy from -1.8 to -2.9) then c-type R R Lyrae stars with periods between 0^35 and 0^37 could also be double-mode candidates. This motivated a search for a secondary oscillation in V38 and V58 (the only stars with periods in the range 0^35-0^37 for which P200 pg data was available). Again the 0 transform of the prewhitened data exihibited no evidence of secondary period (See Fig. 35). In summary, no double-mode R R Lyrae stars were found among the ten candidates for which sufficient data was available. There are eight other R R Lyrae stars that should be checked for a final conclusion about double-mode pulsators in the Ursa Minor dwarf galaxy. These are: V9 , V12, V27, V61, V68, V73, V79 and V81. For these stars only the P60 pg photometry was available and more data are needed. 3.4.4. Anomalous Cepheids in the Ursa Minor dwarf galaxy Anomalous Cepheids are variables with light curves, periods, and amplitudes like those of R R Lyrae stars and short period Population II Cepheids, but are one-half to about two magnitudes brighter than such stars for a given period. Their origin is controversial. Norris and Zinn (1975) and Demarque and Hirschfeld (1975) suggest - 9 6 -that these stars belong to a very young population formed after the main collapse of the dwarf galaxy. Renzini et al. (1977) suggest that anomalous Cepheids are members of old binary systems in which mass transfer has taken place. Wheeler (1979) suggests they may be single stars with extended lifetimes due to internal mixing. Only one anomalous Cepheid has been found in a globular cluster: V19 in N G C 5466 (Zinn and Dahn, 1976 and Zinn and King 1982). Thirty nine anomalous Cepheids have been found among the dwarf spheroidals (plus four new ones in the Ursa Minor dwarf galaxy, from NWO) and six in the Small Magellanic Cloud. However, none have been found in the Large Magellanic Cloud (Graham 1977, 1985; Connolly 1985 and references therein). Anomalous Cepheids have been found in all seven dwarf spheroidal galaxies in the Local Group. Three have been found in the Sculptor dwarf galaxy, one in Fornax, five in Draco, four in Leo II, twelve in Leo I, seven in Carina and seven in the Ursa Minor dwarf galaxy: V6, V56 and V59 from van Agt (1967) and V I , V I 1 , V62 and V80 from N W O . Saha et al. (1986) in his study of the variable stars in the Carina dwarf galaxy observed eight bright variables he thought are in the line of sight to the galaxy. They have absolute magnitudes in the same range as the anomalous Cepheids in other spheroidals. However, it is very difficult to determine the correct period for these stars, since the observations were made in four days in a row causing a strong aliasing problem. Periods were redetermined and, with the exception of V9, all those bright stars in Carina were concluded to be anomalous Cepheids. Swope (1968) lists all the "anomalous Cepheids" (this term was introduced later by Norris and Zinn 1975) discovered in dwarf spheroidals up to that time. Using Swope's list and data on anomalous Cepheids in the Small Magellanic Cloud and N G C 5466, Zinn and Searle (1976) plotted a period-luminosity (P-L) diagram. They showed that the anomalous Cepheids do fit neither the R R Lyrae group nor the population I and II Cepheids. In Zinn's diagram V59 was plotted with the new period derived by Kholopov (P=0^389 and not 0^640 as given by van Agt). In F ig .36 a similar P - L diagram is plotted, including all the new photographic and C C D data for the variables in the Ursa Minor dwarf galaxy. A list of all the anomalous Cepheids identified in dwarf galaxies to date is given in table IX of N W O . Star V6 in the Ursa Minor dwarf galaxy is plotted with the revised period of P=0^725586. The mean absolute B magnitude of the R R Lyrae stars is set at 0™80, corresponding to the mean apparent B magnitude 20^16 (derived using all the R R Lyrae stars in the system, NWO) . The anomalous Cepheids in Leo I (Hodge and Wright 1978) are not plotted due to large uncertainties in the photometry caused by the proximity of that galaxy to the star Regulus. The anomalous Cepheids in Carina are not plotted due to the uncertainties in the periods and absolute magnitudes of the stars. (See N W O for P -L diagrams including Leo I, Carina and S M C anomalous Cepheids). V119 in Sculptor is not in Swope's list. It is plotted in the position log P=0.06 and M#=-0 I ^55. (lower luminosity limit given by Smith and Striker 1986). From the new photographic and C C D data, V59 is ~ 0mA brighter than the mean B magnitude for the six R R Lyrae stars studied here. It fits fairly well in the period-amplitude diagram (NWO) and it could simply be a c-type R R Lyrae star in a more - 9 8 -17.0 18.0 m B 19.0 20.0 21.0 -0.6 -0.3 0.0 0.3 0.6 Log P Fig . 36 — Period-luminosity diagram for the Ursa Minor dwarf galaxy variables (NWO 1988), and the anomalous Cepheids in five dwarf spheroidal galaxies (Swope 1968, Kholopov 1971 Zinn et al. 1976 and Light et al. 1986) and in the globular cluster N G C 5466. Filled and open circles are c and ab type R R Lyrae stars in the Ursa Minor dwarf galaxy, from this study and N W O . V72, the faintest and shortest period R R Lyrae in the system is indicated. The mean absolute B magnitude of the R R Lyraes is set at 0^80, corresponding to the mean apparent B magnitude of 20™16 (NWO). The position of the anomalous Cepheids are indicated with letters. L2's indicate the anomalous Cepheids in Leo II, D's indicate those in Draco, S's those in Sculptor, U's those in Ursa Minor and F that in Fornax. The only globular cluster anomalous Cepheid (V19 in N G C 5466) is also shown. The regions containing population II Cepheids and classical Cepheids were adopted from Zinn and Searle (1976). Clearly, there are two distinct linear relationships for anomalous Cepheids (the equations of the lines are given in NWO) . These distinct lines correspond to anomalous Cepheids pulsating in two different modes: fundamental and first overtone (steeper slope). - 99 -evolved stage of evolution. According to the stellar evolution tracks shown in Figs. 8 and 9 of Sandage (1981b), evolved R R Lyrae stars can be up to 0^5 brighter than horizontal branch stars when they are evolving off the horizontal branch towards the asymptotic giant branch. A n example of that is V47 in to Cen, which has P=0^485 (log P = -0.314). It is ~ 0™35 brighter than the average horizontal branch star (see Fig. 2 of Sandage, 1981a) and it is still classified as an R R Lyrae star. On the other hand, the period and MB of V59 are comparable to those of the anomalous Cepheid V I in Leo II and it lies on the P -L relationship for anomalous Cepheids (see Fig . 36). For this reason it is also classified here as an anomalous Cepheid. The new anomalous Cepheids identified: V I , VI1 V62 and V80 are respectively 0m.5, 0™6, 0^8 and 0m.6 brighter than the horizontal branch stars respectively. The only criterion used to classify these stars as anomalous Cepheids was their position on the period-luminosity diagram (they fit the P - L relationship for anomalous Cepheids). V19, V73 and V79 are 0™20-0 I Ii27 magnitudes brighter than the average magnitude of the R R Lyrae stars in the Ursa Minor dwarf galaxy and they are probably R R Lyrae stars evolving off the horizontal branch. Fig. 36 shows clearly that there are two distinct linear relationships for anoma-lous Cepheids (the equations of the lines are given in NWO) . N W O suggest that these distinct lines correspond to anomalous Cepheids pulsating in two different modes: fun-damental and first-overtone (ab-type and c-type anomalous Cepheids, respectively). Support for this idea is found in the fact that V19, long suspected of being a first-overtone pulsator (Zinn and King 1982), lies along the c-type anomalous Cepheid line. - 100 -The pulsation modes of the Draco anomalous Cepheids suggested by Zinn and Searle (1976) and Cox and Proffitt (1988) are also in agreement with the new relationships found. There also seems to be a correlation between the amplitude of the pulsation, the shape of the light curve and the mode of pulsation for the anomalous Cepheids (Nemec and Simon 1988, unpublished). Bohm-Vitense (1988) finds a similar division among classical Pop I Cepheids. She concludes that all Pop I Cepheids with periods shorter than ~ 7d.O are first-overtone pulsators, and longer period stars pulsate in the fundamental mode. This clean division according to period is not seen among the anomalous Cepheids, where the periods overlap. 3.4.5. Second-Overtone Pulsators in the Ursa Minor dwarf galaxy Fig. 11 in N W O shows the amplitude versus log P diagram (P* = period cor-rected for the luminosity evolution effect, Sandage 1981a) for the R R Lyrae stars in the Ursa Minor dwarf galaxy. A well-defined bimodal distribution of ab-types (fundamental pulsators) and c-types (first-overtone pulsators) is seen. Stars that were initially con-sidered to be candidate second-overtone pulsators because of the possibility that they might have periods between 0d.2 and 0^3, were ultimately classified as first-overtone pulsators. These are stars V3 (P=0^305 or 0^385), V57 (P=0<?288 or 0<*405), V72 (P=0£!204 or 0<*250) and V95 (P=0<*234, 0^305 and 0^439) and they do not fit the c-type distribution if the shorter possible periods are adopted. For V57 and V95 KP36 C C D , P60 pg and P200 pg data are available. Theta transforms and light curves for the most probable periods for these stars were already shown in § 3.3.2. Despite the - 101 -large scatter in the light curves, the longer periods seemed to be favoured. For V3 only P60 pg data were available. The light curves plotted with the two most probable periods look equally plausible and the longer period P=0^385 was chosen because it gives a better fit on the period-amplitude diagram (NWO), if only the ab and c-type RR Lyrae star distributions are considered. For V72 the shorter period P=0*204 gives the less scattered light curve and seems to be the correct period. In summary, V72 is the only candidate for a possible second-overtone pulsator in the Ursa Minor dwarf galaxy. V72 is a unique variable in that it is the shortest period RR Lyrae star in the system, it has very low amplitude, and it is the faintest RR Lyrae (about 0™2 larger than the mean magnitude of the other RR Lyraes in the Ursa Minor dwarf galaxy). Candidate second-overtone pulsators were also identified in others systems but none were confirmed as such. 3.5. SUMMARY Using CCD photometry of 40 stars in a 2#.5 x 4.1 field of the Ursa Minor dwarf spheroidal galaxy, five c-type RR Lyrae stars, one ab-type RR Lyrae star and one anomalous Cepheid have been studied in detail. Combining these data with two inde-pendent sets of photographic data (taken in 1956 and 1984), accurate mean colours and periods for the seven variables were calculated. Accurate magnitudes to V ~ 20™60 for the non-variable stars on the CCD frames were derived. Period searches, light curves and a colour-magnitude diagram for the seven variables are presented. Analysing the new photographic data on the Ursa Minor dwarf galaxy, four new - 102 -anomalous Cepheids were identified bringing to seven the total number of anomalous Cepheid now known in this system. A plot of the period-luminosity diagram including all the anomalous Cepheids identified in dwarf spheroidal galaxies and in N G C 5466 presented a clear bimodal distribution. The two well defined linear relations on the P-L diagram suggest that all known anomalous Cepheids can be classified as either fundamental or first-overtone pulsators. Masses for anomalous Cepheids can then be derived if information on effective temperature and surface gravity is also available. Five of the Ursa Minor anomalous Cepheids are fundamental pulsators and two are first overtones. Combining all the available data for the variables in Ursa Minor, a search for double-mode-RR Lyrae stars was done. 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